researchseminars.org

Tomas Roubicek (Math. Inst. Charles University)
2020-10-12 13:40 - 15:10 UTC
Title: The old Stefan problem in a new mechanical context (https://master.researchseminars.org/talk/NSCM/1/)
by Tomas Roubicek (Math. Inst. Charles University) as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Martin Doskar (Czech Technical University)
2020-10-19 13:40 - 15:10
Title: Micromorphic model for mechanical metamaterials (https://master.researchseminars.org/talk/NSCM/2/)
by Martin Doskar (Czech Technical University) as part of Nečas Seminar on Continuum Mechanics

Abstract
Metamaterials, with their internal composition carefully designed to feature exotic and often counterintuitive properties such as cloaking or band gaps, are the prime example of a pronounced influence of material’s microstructure on its macroscopic response. Regarding mechanical responses, metamaterials have already delivered high stiffness-to-weight ratio, negative compressibility, and tunable auxetic behaviour. These mechanical metamaterials often rely on internal instability mechanisms that trigger transformation of their periodic microstructure into predefined patterns, which introduces strong kinematic coupling among adjacent periodic metamaterial cells and leads to significant size and boundary effects. As a result, the standard first-order computational homogenization fails to provide an effective model of such metamaterials.

This talk presents a micromorphic computational homogenization scheme that has been recently developed specifically for the instability-driven mechanical metamaterials. The scheme introduces characteristic deformation patterns at microscale, whose magnitudes are communicated across adjacent macroscopic material points by scalar modulation fields, which are added to the standard continuum formulation at the macroscale and for which an additional micromorphic-like conservation law emerges at macroscale. Consequently, the presented scheme captures the above-mentioned size effect and boundary layers and accounts for with spatial mixing of multiple patterns. Combined with the bifurcation analysis, the scheme also correctly predicts local to global (i.e. micro vs. macro) buckling transitions.

Edoardo Mainini (University of Genoa)
2020-10-26 14:40 - 16:10
Title: Linearization of finite elasticity (https://master.researchseminars.org/talk/NSCM/3/)
by Edoardo Mainini (University of Genoa) as part of Nečas Seminar on Continuum Mechanics

Abstract
We show some new results about the linearization of finite elasticity by means of Gamma-convergence, including the incompressible case and pure traction problems.

Marco Bresciani (TU Vienna)
2020-11-02 14:40 - 16:10
Title: Linearized von Kármán theory for incompressible magnetoelastic plates (https://master.researchseminars.org/talk/NSCM/4/)
by Marco Bresciani (TU Vienna) as part of Nečas Seminar on Continuum Mechanics

Abstract
We study the asymptotic behavior, in the sense of Gamma-convergence, of a thin incompressible magnetoelastic plate, as its thickness goes to zero. We focus on the linearized von Kármán regime. The model features a mixed Eulerian-Lagrangian formulation, as magnetizations are defined on the deformed configuration.

Daya Reddy (University of Cape Town)
2020-12-21 14:40 - 16:10
Title: Some mathematical aspects of models of strain-gradient plasticity (https://master.researchseminars.org/talk/NSCM/5/)
by Daya Reddy (University of Cape Town) as part of Nečas Seminar on Continuum Mechanics

Abstract
Strain-gradient plasticity has become well established as an approach to modelling seize-dependent phenomena at the meso- and microscales. This presentation is concerned with a class of models of strain-gradient plasticity, which mathematically are formulated as variational inequalities. Conditions for well-posedness are reviewed, following which attention is given to some aspects of what is referred to as the dissipative model. Though in a sense a natural extension of conventional plasticity, this model possesses some distinctive features, most particularly that the plastic flow relations take a global form. The consequences of this feature are discussed, for example, in relation to determining the stage at which incipient plastic behaviour takes place. The presentation also treats issues relevant to approximations, such as the convergence of predictor-corrector algorithms, and approximations under conditions of minimal regularity.

Marco Bravin (BCAM Bilbao)
2020-11-09 14:40 - 16:10
Title: On some properties for an incompressible, non-viscous in-out flow in a 2D domain (https://master.researchseminars.org/talk/NSCM/6/)
by Marco Bravin (BCAM Bilbao) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk I will present some recent results on some properties of an in-out flow
associated with a perfect two dimensional fluid. In particular I present existence of
solutions in different classes of regularity and I will conclude with the study of the
asymptotic limit of some shrinking sources and sinks. This work is motivated by a
question left open by Judovic in [2].
The system consists of an Euler type system in a bounded domain with some holes
where non-homogeneous boundary conditions are prescribed. I will present how to extend some classical existence results in this setting and then I will consider the case
when the holes shrink to points. The boundary conditions lead to the creation of some
point sources and sinks associated with some vortex points in the limit. Similar type of
systems have been already study by Chemetov and Starovoitov in [1], where a different
approximation approach was considered.

References

[1] Chemetov, N. V., Starovoitov, V. N. (2002). On a Motion of a Perfect Fluid in a Domain with Sources and Sinks. Journal of Mathematical Fluid Mechanics, 4(2), 128–144.

[2] Judovic, V. I. (1964). A two-dimensional non-stationary problem on the flow of an
ideal incompressible fluid through a given region. (Russian) Mat. Sb. (N.S.) 64 (106)
562–588

Jacopo Ciambella (Sapienza Università di Roma)
2020-11-16 14:40 - 16:10
Title: Fibre re-orientation in anisotropic viscoelastic materials (https://master.researchseminars.org/talk/NSCM/7/)
by Jacopo Ciambella (Sapienza Università di Roma) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we will derive a nonlinear viscoelastic model for fibre-reinforced materials based on the kinematic assumption that the deformation gradient can be multiplicatively decomposed into viscous and elastic components, i.e., F=Fe Fv. The model is thermodynamically consistent and the evolution equation of the viscous deformation will be derived by combining suitable constitutive prescriptions with balance equations. We will show that, when external sources are absent, an Eshelbian-like torque drives the passive reorientation of the fibres. During the talk, some issues underlying the definition of anisotropic and inelastic models will be discussed, including the evolution of the symmetry group of the material response due to the inelastic relaxation. Finally, some prototype boundary value problems will be presented with the intent of highlighting the best experimental procedure to evaluate the constitutive coefficients of such a model.

‪Giuseppe Tomassetti‬ (Università Roma Tre)
2020-11-30 14:40 - 16:10
Title: Shape programming of a magnetic elastica (https://master.researchseminars.org/talk/NSCM/8/)
by ‪Giuseppe Tomassetti‬ (Università Roma Tre) as part of Nečas Seminar on Continuum Mechanics

Abstract
We consider a cantilever beam which possesses a possibly non-uniform permanent magnetization, and whose shape is controlled by an applied magnetic field. We model the beam as a plane elastic curve and we suppose that the magnetic field acts upon the beam by means of a distributed couple that pulls the magnetization towards its direction. Given a list of target shapes, we look for a design of the magnetization profile and for a list of controls such that the shapes assumed by the beam when acted upon by the controls are as close as possible to the targets, in an averaged sense. To this effect, we formulate and solve an optimal design and control problem leading to the minimization of a functional which we study by both direct and indirect methods. In particular, we prove that minimizers exist, solve the associated Lagrange-multiplier formulation (besides non-generic cases), and are unique at least for sufficiently low intensities of the controlling magnetic fields. To achieve the latter result, we use two nested fixed-point arguments relying on the Lagrange-multiplier formulation of the problem, a method which also suggests a numerical scheme. Various relevant open question are also discussed.

Charlotte Perrin (CNRS Marseille)
2020-11-23 14:40 - 16:10
Title: Compressible Euler equations under a maximal density constraint (https://master.researchseminars.org/talk/NSCM/9/)
by Charlotte Perrin (CNRS Marseille) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, I will present recent results on solutions to a one-dimensional Euler system coupling compressible and incompressible phases. With this original fluid system we intend to model congestion (or saturation) phenomena in heterogeneous flows (mixtures, wave-structure interactions, collective motion, etc.). Here the compressible-incompressible model will be seen as the limit of a fully compressible Euler system endowed with a singular pressure law. The goal of the talk is to present theoretical results concerning this singular limit. This is a joint work with Roberta Bianchini.

Tai-Peng Tsai (University of British Columbia)
2020-12-14 15:30 - 17:00
Title: The Green tensor of the nonstationary Stokes system in the half space (https://master.researchseminars.org/talk/NSCM/10/)
by Tai-Peng Tsai (University of British Columbia) as part of Nečas Seminar on Continuum Mechanics

Abstract
We prove the first-ever pointwise estimates of the (unrestricted) Green tensor and
the associated pressure tensor of the nonstationary Stokes system in the half-space, for
every space dimension greater than one. The force field is not necessarily assumed to
be solenoidal. The key is to find a suitable Green tensor formula that maximizes the
tangential decay, showing in particular the integrability of Green tensor derivatives.
With its pointwise estimates, we show the symmetry of the Green tensor, which in
turn improves pointwise estimates. We also study how the solutions converge to the
initial data, and the (infinitely many) restricted Green tensors acting on solenoidal
vector fields. As applications, we give new proofs of the existence of mild solutions of the
Navier-Stokes equations in Lq, pointwise decay, and uniformly local Lq spaces in the
half-space.
This talk is based on arXiv:2011.00134, a joint work with Kyungkeun Kang, Baishun
Lai and Chen-Chih Lai.

This seminar session will exceptionally start at 16:30.

Arnab Roy (Math. Inst. Czech Academy of Sciences)
2020-12-07 14:40 - 16:10
Title: Existence of strong solutions for a system of interaction between a compressible viscous fluid and a wave equation (https://master.researchseminars.org/talk/NSCM/11/)
by Arnab Roy (Math. Inst. Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we consider a fluid-structure interaction system
where the fluid is viscous and compressible and where the structure is
a part of the boundary of the fluid domain and is deformable. The fluid
is governed by the barotropic compressible Navier-Stokes system whereas
the structure displacement is described by a wave equation. The
reference configuration for the fluid domain is a rectangular cuboid
with the elastic structure being the top face. We use a modified
Lagrangian change of variables to transform the moving fluid domain into
the rectangular cuboid and then analyze the corresponding linear system
coupling a transport equation (for the density), a heat-type equation
and a wave equation. The corresponding results for this linear system
and estimations of the coefficients coming from the change of variables
allow us to perform a fixed point argument and to prove the existence
and uniqueness of strong solutions for the nonlinear system, locally in
time.

Karoline Disser (Universitaet Kassel)
2021-01-04 14:40 - 16:10
Title: Global existence and stability for dissipative processes coupled across volume and surface (https://master.researchseminars.org/talk/NSCM/12/)
by Karoline Disser (Universitaet Kassel) as part of Nečas Seminar on Continuum Mechanics

Abstract
The modelling of technological and biological processes and devices is
often characterized by non-smoothness: material edges and corners,
abruptly changing material properties and a large scope of relevant
temporal and spatial scales. From a PDE point-of-view, we need to deal
with domains of low boundary regularity, mixed and dynamic boundary
conditions, degeneracy and discontinuity of parameters, and, possibly
after rescaling, with the coupling of dynamics across voulme and
lower-dimensional interfaces or surfaces.

In this talk, I want to consider models of non-linear
reaction-drift-diffusion type in non-smooth and/or volume-surface
settings and discuss their analysis based on the choice of specific
functional analytic settings. The aim is to discuss some aspects of the
interaction of thermodynamically consistent modelling and the analysis
of the PDE and to establish strategies for simultaneously dealing with
non-linearity and non-smoothness.

semester break
2021-01-11 14:40 - 16:10, 2021-01-18 14:40 - 16:10, 2021-01-25 14:40 - 16:10, 2021-02-01 14:40 - 16:10, 2021-02-08 14:40 - 16:10, 2021-02-15 14:40 - 16:10, 2021-02-22 14:40 - 16:10
Title: No lecture (https://master.researchseminars.org/talk/NSCM/13/)
by semester break as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Easter Monday
2021-04-05 13:40 - 15:10, 2022-04-18 13:40 - 15:10
Title: No lecture (https://master.researchseminars.org/talk/NSCM/20/)
by Easter Monday as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Jiří Outrata (ÚTIA, Czech Acad. Sci.)
2021-03-01 14:40 - 16:10
Title: On the solution of static contact problems with Coulomb friction via the semismooth* Newton method (https://master.researchseminars.org/talk/NSCM/21/)
by Jiří Outrata (ÚTIA, Czech Acad. Sci.) as part of Nečas Seminar on Continuum Mechanics

Abstract
The lecture deals with application of a new Newton-type method to the numerical solution of discrete 3D contact problems
with Coulomb friction. This method suits well to the solution of inclusions and the resulting conceptual algorithm exhibits,
under appropriate conditions, the local superlinear convergence. After a description of the method a new (primal) model
for the considered contact problem, amenable to the application of the new method, will be presented. The second part of
the talk is then devoted to an efficient implementation of the general algorithm and to numerical tests. Throughout the whole
lecture, various tools of modern variational analysis will be employed.

Malte Kampschulte (Charles University)
2021-03-22 14:40 - 16:10
Title: Minimizing movements and a two-scale method for nonconvex problems involving inertia (https://master.researchseminars.org/talk/NSCM/22/)
by Malte Kampschulte (Charles University) as part of Nečas Seminar on Continuum Mechanics

Abstract
When dealing with fully nonlinear, nonconvex, quasistatic (i.e. inertialess) problems in continuum mechanics, de Giorgi's method of minimizing movements has long been a staple for existence proofs. However by its very nature, it has always been restricted to purely dissipative, gradient flow-type systems. The aim of this talk is to present a new two-scale method, developed jointly with B. Benešová and S. Schwarzacher, which allows to add inertial, conservative effects by using the minimizing movements method as a stepping stone to solve an approximative time-delayed problem in the same nonlinear, nonconvex state space. Using a flow-map approach, this method is not only able to cope with problems in Lagrangian, but also with those in Eulerian and even mixed formulations. While the method itself is quite general, we will illustrate its application at several examples involving solids, fluids and their interaction.

Eitan Tadmor (University of Maryland, College Park)
2021-03-29 13:40 - 15:10
Title: Emergent behavior in swarming hydrodynamics (https://master.researchseminars.org/talk/NSCM/23/)
by Eitan Tadmor (University of Maryland, College Park) as part of Nečas Seminar on Continuum Mechanics

Abstract
I will discuss recent developments in our study of swarming
dynamics.
A main question of interest is the emergent behavior which we
characterize by
spectral analysis, covering different classes of long-range and
short-range communication kernels.
These include examples of metric-based and topologically-based kernels,
and kernels derived from a unified paradigm of anticipation.
In the canonical case of metric-based short-range kernels, we derive
lower-bounds on the spectral gap,
independent of thermal equilibrium (no closure for the pressure), which
yield an emergent behavior of non-vacuous smooth solutions.
The latter are known to exist in one- and two space dimensions and we
settle the question of existence for arbitrary dimension.

Antonio J. Gil (University of Swansea, UK)
2021-03-08 14:40 - 16:10
Title: On the use of mixed formulations for computational polyconvexity and multi-variable convexity (https://master.researchseminars.org/talk/NSCM/24/)
by Antonio J. Gil (University of Swansea, UK) as part of Nečas Seminar on Continuum Mechanics

Abstract
The computational modelling of large strain multi-physics problems is nowadays an area of intensive research by numerous scientists. Among problems of this kind, two pressing applications underpin the motivation behind this presentation. On the one hand, the in-silico design of highly flexible dielectric elastomers for soft robotics applications and, on the other hand, the realistic simulation of the electromechanical interactions of the cardiac muscle from the physiological and pathological standpoints. In both applications, the requirement for extremely accurate and stable results at, possibly, large values of the field variables (i.e. strains and electric/cardiac potential) proves very challenging from the computational point of view.
The presentation starts by revisiting the now well-accepted requirement of polyconvexity (a sufficient condition for rank-one convexity) in the case of reversible hyperelasticity, where the strain energy functional is described by a convex combination of the minors of the deformation gradient tensor. We then extend this concept to the case of energies which depend on non-strain based variables, for instance, other physical measures such as the electric displacement, leading to the introduction of a new computational paradigm, Multi-Variable Convexity. Crucially, this new definition of the internal energy enables ellipticity to be extended to the entire range of deformations and electric fields and, thus, spurious numerical instabilities can then effectively be removed from the model whilst maintaining real physical instabilities.
The polyconvexity of the energy functional with respect to its set of arguments guarantees the definition of well-posed counterpart work conjugates, where a one to one (invertible) relationship can be established. This ensures the existence of alternative energy potentials via the use of partial or total Legendre transforms and opens up the possibility for new extended Hu–Washizu-type variational principles in terms of using various interpolation spaces for the different unknown fields, leading to enhanced type of formulations. A series of examples will be presented demonstrating the potential of this new paradigm when coupled with the use of Finite Element type discretisation techniques.

Adrian Muntean (Karlstadt University)
2021-04-26 13:40 - 15:10
Title: Does vesicle micro-dynamics enhance the signaling among plants macro-transport? Multiscale discussions around a model problem (https://master.researchseminars.org/talk/NSCM/25/)
by Adrian Muntean (Karlstadt University) as part of Nečas Seminar on Continuum Mechanics

Abstract
We study a transport problem for signaling among plants in the context of measure-valued equations. We report on preliminary results concerning the modeling and mathematical analysis of a reaction-diffusion scenario involving the macroscopic diffusion of signaling molecules enhanced by the presence of a finite number of microscopic vesicles - pockets with own dynamics able to capture and release signals as a relay system. The coupling between the macroscopic and microscopic spatial scales relies on the use of a two-scale transmission condition and benefits of the posing of the problem in terms of measures. Mild solutions to our problem will turn to exist and will also be positive weak solutions. A couple of open questions at the modeling, mathematical analysis, and simulation levels will be pointed out. This is a joint work with Sander Hille (Leiden, NL) and is supported financially by the KVA’s G. S. Magnussonsfond.

Valerio Pagliari (TU Vienna)
2021-04-12 13:40 - 15:10
Title: Convergence of nonlocal geometric flows to anisotropic mean curvature motion (https://master.researchseminars.org/talk/NSCM/26/)
by Valerio Pagliari (TU Vienna) as part of Nečas Seminar on Continuum Mechanics

Abstract
We consider the Cauchy problem for motions by nonlocal curvature, whose
well-posedness may be established in the framework of viscosity solutions.
We show that a suitable rescaling of the nonlocal curvature induces a
localisation effect, that is, as the scaling parameter tends to 0,
we retrieve an anisotropic mean curvature functional. From this fact,
thanks to the theory of geometric barriers by De Giorgi,
we prove that the solutions to the rescaled nonlocal motions locally
uniformly converge to the solution of the local flow.
The talk is based on joint work with A. Cesaroni (Padova).

‪Denis Bonheure (Université Libre de Bruxelles)
2021-05-10 13:40 - 15:10
Title: Equilibrium configuration of a rectangular obstacle immersed in a channel flow (https://master.researchseminars.org/talk/NSCM/27/)
by ‪Denis Bonheure (Université Libre de Bruxelles) as part of Nečas Seminar on Continuum Mechanics

Abstract
Fluid flows around an obstacle generate vortices which, in turn, generate lift forces on the obstacle. Therefore, even in a perfectly symmetric framework equilibrium positions may be asymmetric. We show that this is not the case for a Poiseuille flow in an unbounded 2D channel, at least for small Reynolds number and flow rate. We consider both the cases of vertically moving obstacles and obstacles rotating around a fixed pin.
Joint work with P.G. Galdi and F. Gazzola

Maria Neuss-Radu (University of Erlangen-Nuremberg)
2021-05-24 13:40 - 15:10
Title: Homogenization of a reaction-diffusion-advection problem in an evolving micro-domain and including nonlinear boundary conditions (https://master.researchseminars.org/talk/NSCM/28/)
by Maria Neuss-Radu (University of Erlangen-Nuremberg) as part of Nečas Seminar on Continuum Mechanics

Abstract
We consider a reaction-diffusion-advection problem in a
perforated medium, with nonlinear reactions in the bulk and at the
microscopic boundary, and slow diffusion scaling. The microstructure
changes in time; the microstructural evolution is known a priori. The
aim of the paper is the rigorous derivation of a homogenized model. We
use appropriately scaled function spaces, which allow us to show
compactness results, especially regarding the time-derivative and we
prove strong two-scale compactness results of Kolmogorov-Simon-type,
which allow to pass to the limit in the nonlinear terms. The derived
macroscopic model depends on the micro- and the macro-variable, and the
evolution of the underlying microstructure is approximated by time- and
space-dependent reference elements. This is a joint work with Markus
Gahn (University of Heidelberg) and Iuliu Sorin Pop (Hasselt
University).

Patrick Dondl (University of Freiburg)
2021-03-15 14:40 - 16:10
Title: Energetic bounds for paperboard delamination under bending (https://master.researchseminars.org/talk/NSCM/29/)
by Patrick Dondl (University of Freiburg) as part of Nečas Seminar on Continuum Mechanics

Abstract
Paperboard is an engineering material consisting of a number of separate sheets of paper, that have been bonded together. Experimental evidence shows that paperboard undergoing bending develops phenomenologically plastic hinges. We consider a nonlinearly elastic mathematical model for paperboard, allowing debonding of the sheets at a given cost per unit area. Analysis of our model predicts a number of different regimes, including somewhere bending is concentrated in delaminated hinges, where the mid-plane of each individual layer may deform isometrically. This is joint work with Sergio Conti (Bonn) and Julia Orlik (Kaiserslautern).

Summer break
2021-06-07 13:40 - 15:10
Title: We'll meet again in October 2021 (https://master.researchseminars.org/talk/NSCM/30/)
by Summer break as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Jan Březina (TU Liberec)
2021-05-03 13:40 - 15:10
Title: Continuum-fracture approach to modelling crystalline rock (https://master.researchseminars.org/talk/NSCM/31/)
by Jan Březina (TU Liberec) as part of Nečas Seminar on Continuum Mechanics

Abstract
We start with a statistical description of the fracture networks in real (crystalline) rocks and related heterogeneous material properties. Next, we shall present continuum-fracture (CF) approach to the description of the processes in real rock. CF description has been consistently applied in the Flow123d simulator of THMC proceses. We will summarize simulated processes, numerical schemes, and software tools. Finally, we present particular applications in the safety of deep nuclear waste repositories and the efficiency of enhanced geothermal systems.

Jan Stebel (TU Liberec)
2021-05-17 13:40 - 15:10
Title: Continuum-fracture models of porous media processes: derivation and analysis (https://master.researchseminars.org/talk/NSCM/32/)
by Jan Stebel (TU Liberec) as part of Nečas Seminar on Continuum Mechanics

Abstract
Mathematical modelling of heterogeneous materials such as granitic rocks requires special treatment of fractures. We present the derivation of the so-called continuum-fracture model for two types of problems: advection-diffusion process (e.g. transport of contaminants or heat) and hydro-mechanical coupling based on Biot’s theory. For the hydro-mechanical problem we distinguish the linear case and the case of contact and shear-dilation conditions at fractures. Existence of weak solutions is established. The problem is discretized by the finite element method and solved using the so-called fixed-stress iterative splitting whose convergence is analyzed.

Milan Pokorný (Mathematical Institute, Charles Universiy)
2021-05-31 13:40 - 15:10
Title: Homogenization of Navier--Stokes--Fourier system in domains with tiny holes (https://master.researchseminars.org/talk/NSCM/33/)
by Milan Pokorný (Mathematical Institute, Charles Universiy) as part of Nečas Seminar on Continuum Mechanics

Abstract
We consider the compressible Navier--Stokes--Fourier system in a domain with large number of holes. Under the assumption that the holes are sufficiently small, together with certain standard assumptions on the adiabatic exponent and the behaviour of the heat conductivity, we show that if passing simultaneously with the number of holes to infinity and their size to zero, in the limit we obtain again solution to the compressible Navier--Stokes--Fourier system in the domain without holes. The result holds both for the steady and evolutionary problem. It is a joint work with Yong Lu (Nanjing University) and Emil Skříšovský (Charles University, Prague).

Manuel Friedrich (University of Muenster)
2021-04-19 13:40 - 15:10
Title: Emergence of rigid polycrystals from atomistic systems (https://master.researchseminars.org/talk/NSCM/34/)
by Manuel Friedrich (University of Muenster) as part of Nečas Seminar on Continuum Mechanics

Abstract
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the `sticky disk’ interaction potential models the atoms as hard spheres that interact when they are tangential. The discrete energy is frame invariant and no underlying reference lattice on the atomistic configurations is assumed. By means of Gamma-convergence, we characterize the asymptotic behavior of configurations with finite surface energy scaling in the infinite particle limit. The effective continuum theory is described in terms of a piecewise constant field delineating the local orientation and micro-translation of the configuration. The limiting energy is local and concentrated on the grain boundaries, i.e., on the boundaries of the zones where the underlying microscopic configuration has constant parameters. The corresponding surface energy density depends on the relative orientation of the two grains, their microscopic translation misfit, and the normal to the interface. Joint work with Leonard Kreutz (Münster) and Bernd Schmidt (Augsburg).

Jan Zeman (Faculty of Civil Engineering, Czech Tech. Uni.)
2021-10-04 13:40 - 15:10
Title: Designing optimal reinforcement for high-performance composite tubes with semidefinite programming (https://master.researchseminars.org/talk/NSCM/35/)
by Jan Zeman (Faculty of Civil Engineering, Czech Tech. Uni.) as part of Nečas Seminar on Continuum Mechanics

Lecture held in K3 Karlin.

Abstract
Fueled by their excellent stiffness-to-weight ratio and the availability of mature manufacturing technologies, filament wound carbon fiber reinforced polymers represent ideal materials for thin-walled laminate structures. However, their strong anisotropy reduces structural resistance to wall instabilities under shear and buckling. Increasing laminate thickness degrades weight and structural efficiencies and the application of a dense internal core is often uneconomical and labor-intensive. In this contribution, we introduce a convex linear semidefinite programming formulation for truss topology optimization to design an efficient non-uniform lattice-like internal structure. The internal structure not only reduces the effect of wall instabilities, mirrored in the increase of the fundamental free-vibration eigenfrequency, but also keeps weight low, secures manufacturability using conventional three-dimensional printers, and withstands the loads induced during the production process. We showcase a fully automatic procedure in detail for the design, prototype manufacturing, and verification of a simply-supported composite machine tool component, including validation with roving hammer tests. The results confirm that the 3D-printed optimized internal structure almost doubles the fundamental free-vibration eigenfrequency, allowing to increase the working frequency of the machine tool, even though the ratio between elastic properties of the carbon composite and the ABS polymer used for 3D printing exceeds two orders of magnitude.

Hanuš Seiner (Inst. of Thermomechanics, CAS)
2021-10-18 13:40 - 15:10
Title: Landau-energy landscape reconstruction for a Ni-Fe-Ga(Co) Shape Memory Alloy (https://master.researchseminars.org/talk/NSCM/36/)
by Hanuš Seiner (Inst. of Thermomechanics, CAS) as part of Nečas Seminar on Continuum Mechanics

Abstract
In the framework of continuum mechanics, the thermo-mechanical behavior of shape memory alloys is often described using the Landau-theory approach, where the multi-well free energy density of the crystal is approximated by a polynomial with the required number of minima and energy barriers. Here we show how the energy landscape (in the strain-temperature space) can be reconstructed from experiments, and how accurately this energy is approximated by the Landau-theory ansatz. Elastic behavior of single crystals of Ni-Fe-Ga(Co) ferromagnetic shape memory alloys is studied in a broad temperature range. Using tensile stress-strain measurements and ultrasonic characterization, we prove that austenite and martensite phases of the given alloy exhibit strongly non-linear elastic responses, and we utilize the non-linear stress-strain data for constructing an energy function describing the observed behavior in the context of the Landau theory. We discuss the implications of the constructed model, focusing in particular to the so-called critical point in the energy landscape, where the austenite-martensite transition becomes weakly second-order.

Katharina Brazda (University of Vienna)
2021-10-25 13:40 - 15:10
Title: Multiphase biological membranes (https://master.researchseminars.org/talk/NSCM/37/)
by Katharina Brazda (University of Vienna) as part of Nečas Seminar on Continuum Mechanics

Lecture held in K3 Karlin, Sokolovska 83, Praha 8.

Abstract
Biological membranes are thin layers of lipid molecules. Mechanically,
they can be described as incompressible viscous fluid surfaces with
bending elasticity. The equilibrium shapes of homogeneous membranes
minimize the Canham-Helfrich energy under area and enclosed volume
constraints. In particular, this variational model explains the typical
biconcave shape of human red blood cells. Configurations of
heterogeneous biomembranes also feature an intriguing coupling effect
between composition and geometry, which originates from their inherent
fluidity. In this talk, we introduce these models and present an
existence result for multiphase membranes with sharp phase interfaces,
obtained in the framework of oriented curvature varifolds.

Filippo Riva (University of Pavia)
2021-10-11 13:40 - 15:10
Title: Inertial Balanced Viscosity solutions to rate-independent systems (https://master.researchseminars.org/talk/NSCM/38/)
by Filippo Riva (University of Pavia) as part of Nečas Seminar on Continuum Mechanics

Abstract
Rate-independent evolutions frequently occur in mechanics when
the problem
under consideration presents such small rate-dependent effects, as
inertia or viscosity, that can be neglected. If the driving potential
energy is nonconvex any (reasonable) solution necessarily exhibits
time-discontinuities. To describe the behaviour of the jumps, in the
last decades the notions of Energetic and Balanced Viscosity solutions
have been developed, the latter as a refinement of the former. While for
Energetic solutions the cost at jumps is described only in terms of the
rate-independent dissipation potential, in the case of Balanced
Viscosity solutions it arises from a suitable coupling between this
dissipation potential and a smaller and smaller viscosity potential,
which is reminiscent of an original presence of viscous damping.
In this talk we present a novel notion of solution to rate-independent
systems, named Inertial Balanced Viscosity (IBV) solution, which in
addition takes into account small inertial effects. Differently from the
previous cases, now the jump cost turns out to be rate-dependent. In
finite dimension, we show how IBV solutions can be obtained as a
vanishing inertia and viscosity limit of dynamic evolutions, and we
introduce a multiscale Minimizing Movements algorithm which can be used
to build such solutions.
This is a joint work with G. Scilla and F. Solombrino.

Jonathan Bevan (University of Surrey, GB)
2021-11-08 14:40 - 16:10
Title: Interior 'buckling' and non-uniqueness in a class of incompressible variational problems (https://master.researchseminars.org/talk/NSCM/39/)
by Jonathan Bevan (University of Surrey, GB) as part of Nečas Seminar on Continuum Mechanics

Abstract
The talk is about a class variational problems whose associated energies $E_{\eps}$ can be thought of as perturbations of the Dirichlet energy. These energies have countably many pairs of planar, measure-preserving stationary points $u^n_{\pm}$ with the properties that (a) $E_{\eps}(u^n_+)=E_{\eps}(u^n_-)$ and (b) the maps $u^n_{\pm}$ cause `buckling' at the centre $0$ of the unit ball $B$ in $\mathbb{R}^2$ while acting as the identity on $\partial B$. Numerical calculations show that $n$ can be treated as a proxy for the `number of buckles' that occur at $0$, and that, as one might expect, $E_{\eps}(u^n_{\pm})$ increases as $n$ does. This is joint work with J. Deane.

Daniel Campbell (Universita Hradec Králové)
2021-11-29 14:40 - 16:10
Title: Closures of planar BV homeomorphisms and the relaxation of functionals with linear growth (https://master.researchseminars.org/talk/NSCM/40/)
by Daniel Campbell (Universita Hradec Králové) as part of Nečas Seminar on Continuum Mechanics

Abstract
Motivated by relaxation results of Kristensen and Rindler, and of Benešová, Krömer and Kružík for BV maps, we study the class of strict limits of BV planar homeomorphisms. We show that, although such maps need not be injective and are not necessarily continuous on almost every line, the class has a reasonable behavior expected for limit of elastic deformations. By a characterization of the classes of strict and area-strict limits of BV homeomorphisms we show that these classes coincide.

This is based on joint works with S. Hencl, A. Kauranen and E. Radici.

Ulisse Stefanelli (University of Vienna)
2021-11-22 14:40 - 16:10
Title: Existence results for a morphoelastic model (https://master.researchseminars.org/talk/NSCM/41/)
by Ulisse Stefanelli (University of Vienna) as part of Nečas Seminar on Continuum Mechanics

Abstract
I will report on a recent work in collaboration with Elisa Davoli (TU Wien) and Katerina Nik (University of Vienna) on a three-dimensional quasistatic morpholelastic model. The mechanical response of the body and its growth are modeled by an interplay of hyperelastic energy minimization and growth dynamics. A first existence result is obtained by regularization and time-discretization, also taking advantage of an exponential-update scheme. We then allow the growth dynamics to depend on an additional scalar field, say a nutrient, and formulate an optimal control problem. Eventually, we tackle the existence of coupled morphoelastic and nutrient solutions, when the latter is allowed to diffuse and interact with the growing body.

The preprint is available as arXiv:2110.05566.

Tomáš Roubíček (Math. Inst. of Charles University)
2021-11-01 14:40 - 16:10
Title: Visco-plastic elastodynamics and poro-elastodynamics at large deformations by Eulerian approaches (https://master.researchseminars.org/talk/NSCM/42/)
by Tomáš Roubíček (Math. Inst. of Charles University) as part of Nečas Seminar on Continuum Mechanics

Abstract
Two models of hardening-free plasticity at large deformations
will be presented in Eulerian rate formulation based on two
standard concepts, Green-Naghdi additive decomposition
and Kroner-Lee-Liu multiplicative decomposition of the
total strain. Extension towards poroelasticity and
thermodynamics will be outlined, too.

Philipp Reiter (TU Chemnitz)
2021-11-15 14:40 - 16:10
Title: Symmetric elastic knots (https://master.researchseminars.org/talk/NSCM/43/)
by Philipp Reiter (TU Chemnitz) as part of Nečas Seminar on Continuum Mechanics

Abstract
Minimizing the bending energy within knot classes leads to the concept
of elastic knots. Motivated by numerical experiments we prescribe
dihedral symmetry and establish existence of dihedrally symmetric
elastic knots for knot classes admitting this type of symmetry. Among
other results we prove that the dihedral elastic trefoil is the union of
two circles that form a (planar) figure-eight. We also discuss some
generalizations and limitations regarding other symmetries and knot classes.

This is joint work with Alexandra Gilsbach and Heiko von der Mosel.

Stanislav Sysala (Institute of Geonics, Cz. Acad. Sci.)
2021-12-06 14:40 - 16:10
Title: Saddle-point problems with bilinear Lagrangian and convex constraints: analysis, numerical solution and applications (https://master.researchseminars.org/talk/NSCM/44/)
by Stanislav Sysala (Institute of Geonics, Cz. Acad. Sci.) as part of Nečas Seminar on Continuum Mechanics

Abstract
The first part of the talk is concerned with an abstract inf-sup problem
generated by a bilinear Lagrangian and convex constraints. The
conditions that guarantee no gap between the inf-sup and related sup-inf
problems are studied. A particular attention is devoted to the inf-sup
condition defined for convex cones in function spaces. Next, a
regularization method convenient for solving the inf-sup problem is
analyzed and a computable majorant of the critical (inf-sup) value is
derived for purposes of a posteriori error analysis of numerical
results. The second part of the talk is devoted to applications of the
abstract framework to continuum mechanics. In particular, examples of
limit load problems and similar ones arising in classical plasticity,
gradient plasticity and delamination are introduced. The presented
results follow from the joint work with Daya B. Reddy, Sergey Repin and
Jaroslav Haslinger.

Amrita Gosh (University of Bonn)
2021-12-13 14:40 - 16:10
Title: On Shikhmurzaev’s approach to the Contact Line Problem (https://master.researchseminars.org/talk/NSCM/45/)
by Amrita Gosh (University of Bonn) as part of Nečas Seminar on Continuum Mechanics

Abstract
I will discuss the general moving contact line problem, arising from many fluid mechanics
phenomena. The classical formulation of this model with the no-slip (Dirichlet) boundary
condition for velocities at the liquid-solid interface gives rise to a non-integrable singularity
of the shear stress, which is known as the ”moving contact line paradox”. Y. Shikhmurzaev
proposed (1993) a different approach to solve this issue. This approach, apart from the
classical conservation equations, formulates the boundary conditions for the equations in
the bulk phases in an elaborate way, which can be viewed as a generalization of the existing
models in the literature, although generated from a different underlying theory. After giving
an overview of this model, I would like to derive a thin film approximation of Shikhmurzaev’s
model to compare with the other solution model of the contact line problem.

Christmas break (Christmas break)
2021-12-27 14:40 - 16:10, 2021-12-20 14:40 - 16:10
Title: Christmas break (https://master.researchseminars.org/talk/NSCM/46/)
by Christmas break (Christmas break) as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Karel Tůma (Mathematical Institute, Charles University)
2022-01-03 14:40 - 16:10
Title: Finite strain phase-field model for martensitic transformation: Large-scale finite element simulations (https://master.researchseminars.org/talk/NSCM/48/)
by Karel Tůma (Mathematical Institute, Charles University) as part of Nečas Seminar on Continuum Mechanics

Abstract
Martensitic transformation is a first-order solid-solid diffusionless transformation that occurs between the parent phase (austenite) and the product phase (martensite) and is characterized by the microstructure evolution, which is accompanied by the formation, propagation, and annihilation of the interfaces. In shape memory alloys, the microstructure evolution is the mechanism behind the properties such as pseudoelasticity and shape memory effect. In general, due to the incompatibility between austenite and a single variant of martensite, the martensitic transformation is realized via the formation of complex twinning microstructure.
A recently developed phase-field model for multivariant martensitic transformation is implemented using the finite element method and used to compute large-scale simulations reaching 150 million degrees of freedom. The computational problems are quite expensive due to the fact that high mesh density is needed to capture the detailed microstructure, see attached figure. Our implementation has shown robustness and good parallel scaling performance. Having this model, the goal is to perform a systematic investigation of the effect of crystal lattice orientation and material anisotropy on the indentation-induced microstructure evolution in CuAlNi shape memory alloy. To our knowledge, such a comprehensive high-resolution microstructure-based modeling study has not been reported before. This is a joint work with M. Rezaee-Hajidehi, S. Stupkiewicz, J. Hron and P. Farrell.

semester break
2022-01-10 14:40 - 16:10, 2022-01-17 14:40 - 16:10, 2022-01-24 14:40 - 16:10, 2022-01-31 14:40 - 16:10, 2022-02-07 14:40 - 16:10
by semester break as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Sabrine Chebbi (University of Tunisia, El MANAR, UTM)
2022-02-21 14:40 - 16:10
Title: The Energy decay rate of 1D and 2D Timoshenko systems. Theoretical analysis and numerical simulation (https://master.researchseminars.org/talk/NSCM/54/)
by Sabrine Chebbi (University of Tunisia, El MANAR, UTM) as part of Nečas Seminar on Continuum Mechanics

Abstract
We focus on the behavior of the solutions of the Timoshenko systems
in dimensions 1 and 2 using the lower bound estimates of the energy. We
study a nonlinear damped one-dimensional thermo-elastic Timoshenko system
where the heat flux is given by the Cattaneo’s law. After deriving the strong
lower energy estimates, we show the optimality for some explicit examples.
Furthermore, we discuss the well-posedness and the decay rate of the energy
of the Mindlin-Timoshenko plate equations subject to a nonlinear dissipation
acting on the rotation angles’equations. Later, we perform a numerical sim-
ulation of the one-dimensional Timoshenko system, our approach is based
on adequate use of the finite element and the finite difference methods
giving rise to a new scheme which characterizes the asymptotic behavior of
the discrete energy.

Giusy Mazzone (Queen's University)
2022-05-02 13:40 - 15:10
Title: On partially dissipative systems (https://master.researchseminars.org/talk/NSCM/55/)
by Giusy Mazzone (Queen's University) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we will investigate the dynamics of three mechanical systems: a rigid body with a damper, a system of rigid bodies with a fluid-filled gap, and a harmonic oscillator in a fluid-filled pipe. The equations governing the motion of these systems are “partially dissipative”, in that there exists an energy functional that decreases along the trajectories, while other physical variables are conserved or even excited during the motion. The objective of our investigations is to describe the “stabilization properties” of the systems. By “stabilization” we mean either convergence of each trajectory to a stationary solution or the existence of periodic solutions to the governing equations corresponding to forces with arbitrary frequencies.

Petr Pelech (WIAS Berlin)
2022-03-07 14:40 - 16:10
Title: Penrose-Fife model with activated phase transformation - Existence and effective model for slow-loading regimes. (https://master.researchseminars.org/talk/NSCM/56/)
by Petr Pelech (WIAS Berlin) as part of Nečas Seminar on Continuum Mechanics

Abstract
We study a non-autonomous system of two evolutionary PDEs, an enhanced version of the Penrose-Fife model introduced in 1990, which first in history coupled the Allen-Cahn phase-field equation with thermal effects in a thermodynamically consistent way. In our work we consider an activated phase transformation which makes the phase-field equation non-linear in time derivative; it contains an additional term that describes also the Coulomb dry friction and whose analogues appear in rate-independent models of plasticity or damage. Apart from proving the existence of solutions of the system, we investigate its effective behavior for the so-called slow-loading regimes. There the internal time-scale introduced by phase-field viscosity and thermal conductivity is much smaller than the time-scale of the loading, an external force acting on the system. Hence the system stays almost in its equilibrium described by the static solution. However, the limit of solutions (as the ratio of the time scales tends to zero) may not be characterized by the corresponding rate-independent model where the viscous-like terms have been dropped. The reason is that the phase transformation is driven by a non-convex thermodynamic potential and hence the solutions may develop jumps in the limit. In order to resolve the jump's detailed trajectory, along which the viscous effects play a crucial role, we use the so-called Balanced-Viscosity (BV) solutions introduced by Efendiev and Mielke in 2006. This work is a collaboration with Matthias Liero and Alexander Mielke from WIAS Berlin.

Penrose O., Fife P. C. - Thermodynamically Consistent Models of Phase-Field Type for the Kinetics of Phase Transitions (1990)

Sprekels J., Zheng S. M. - Global smooth solutions to a thermodynamically consistent model of phase-field type in higher space dimensions (1993)

Efendiev M., Mielke A. - On the rate-independent limit of systems with dry friction and small viscosity (2006)

Mielke A., Roubicek T. - Rate-independent Systems Theory and Application (2015)

George Avalos (UNIVERSITY of NEBRASKA–LINCOLN)
2022-05-16 13:40 - 15:10
Title: Concerning the strong and uniform decay of solutions to coupled fluid/multilayered structure PDE dynamics (https://master.researchseminars.org/talk/NSCM/58/)
by George Avalos (UNIVERSITY of NEBRASKA–LINCOLN) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we will discuss our recent work on a certain
multilayered structure-fluid interaction (FSI) which arises in the
modeling of vascular blood flow. The coupled PDE system under our
consideration mathematically accounts for the fact that mammalian
veins and arteries are typically composed of various layers of
tissues: each layer will generally manifest its own intrinsic material
properties, and will moreover be separated from the other layers by
thin elastic laminae. Consequently, the resulting modeling FSI system
will manifest an additional PDE, which evolves on the boundary
interface, so as to account for the thin elastic layer. (This is in
contrast to the FSI PDE’s which appear in the literature, wherein
elastic dynamics are largely absent on the boundary interface.) As
such, the PDE system will constitute a coupling of 3D fluid-2D
elastic-3D elastic dynamics. For this multilayered FSI system, we will
in particular present results of strong stability for finite energy
solutions, and polynomial decay for sufficiently regular solutions.
This is joint work with Pelin Güven Geredeli and Boris Muha.

summer break
2022-05-23 13:40 - 15:10
Title: We will continue on Monday, October 3, 2022 (https://master.researchseminars.org/talk/NSCM/59/)
by summer break as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Václav Mácha (Inst. of Mathematics, Czech Academy of Sciences)
2022-02-28 14:40 - 16:10
Title: Fluids in moving domains (https://master.researchseminars.org/talk/NSCM/60/)
by Václav Mácha (Inst. of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Abstract
We present several results concerning the flow of a
compressible heat-conducting fluid in a moving domain. We discuss the
existence of a weak solution. Next, we tackle the low-Mach number
limit and we deduce the target system for the low-stratification case.
The talk is based on results obtained in collaboration with O. Kreml,
S. Nečasová and A. Wroblewska-Kaminska

Justyna Ogorzaly (Jagiellonian University)
2022-04-04 13:40 - 15:10
Title: Variational-Hemivariational Inequalities with Applications to Contact Mechanics (https://master.researchseminars.org/talk/NSCM/61/)
by Justyna Ogorzaly (Jagiellonian University) as part of Nečas Seminar on Continuum Mechanics

Abstract
We will present the existence and uniqueness results for the
special classes of nonlinear variational-hemivariational inequalities.
Then, we will consider concrete contact problems and we will show how
these problems lead to the different type of variational-hemivariational
inequalities.

Henrik Schumacher (TU Chemnitz)
2022-05-09 13:40 - 15:10
Title: Repulsive Curves and Surfaces (https://master.researchseminars.org/talk/NSCM/62/)
by Henrik Schumacher (TU Chemnitz) as part of Nečas Seminar on Continuum Mechanics

Abstract
Functionals that penalize bending or stretching of a surface play a key role in geometric and scientific
computing, but to date have ignored a very basic requirement: in many situations, surfaces must not pass
through themselves or each other. This paper develops a numerical framework for optimization of surface
geometry while avoiding (self-)collision. The starting point is the tangent-point energy, which effectively pushes
apart pairs of points that are close in space but distant along the surface. We develop a discretization of
this energy for triangle meshes and introduce a novel acceleration scheme based on a fractional Sobolev inner
product. In contrast to similar schemes developed for curves (cf. [2]), we avoid the complexity of building a
multiresolution mesh hierarchy by decomposing our preconditioner into two ordinary Poisson equations, plus
forward application of a fractional differential operator. We further accelerate this scheme via hierarchical
approximation and describe how to incorporate a variety of constraints (on area, volume, etc.). Finally, we
explore how this machinery might be applied to problems in mathematical visualization, geometric modeling,
and geometry processing.
Joint work with: Chris Yu, Caleb Brakensiek, Keenan Crane
References
[1] C. Yu, C. Brakensiek, H. Schumacher, and C. Keenan Repulsive Surfaces. ACM Trans. Graph., 40(6):1–19,
2021.
[2] C. Yu, H. Schumacher, and C. Keenan Repulsive Curves. ACM Trans. Graph., 40(2):1-21, 2021.

Marta Zoppello (DISMA, Politecnico di Torino)
2022-03-28 13:40 - 15:10
Title: N-link swimmers swimming alone or in pairs (https://master.researchseminars.org/talk/NSCM/65/)
by Marta Zoppello (DISMA, Politecnico di Torino) as part of Nečas Seminar on Continuum Mechanics

Abstract
This talk presents two models of swimmers immersed in a low Reynolds number fluid,
both of them involving the so-called N -link swimmer. The first one studies the 3-dimensional N-link swimmer swimming alone [1], the second focuses on two planar 2-link swimmers
swimming together [2]. Both models rely on Resistive Force Theory, which is a good approximation of hydrodynamic forces at low Reynolds number for slender swimmers and allows us to cast the equations of motion as ODEs. These equations can be seen as control systems
where the controls are the velocity of deformation of the swimmers.
We prove that the 3 dimensional N -link swimmer is fully controllable and we show the existence of optimal controls for some cost functionals. Regarding the coupled swimmers, even
if, taken singularly, they are non-controllable units (because of Purcell’s celebrated Scallop Theorem), we prove that taking into account the hydrodynamic interaction they can achieve a net motion after a periodic sequence of shape changes. Moreover, under suitable
approximations, we are able to optimize the displacement.

[1] R. Marchello, M, Morandotti, H. Shum, M. Zoppello.
The N -link swimmer in three dimensions: controllability and optimality results.
Accepted for publication in Acta Applicandae Mathematicae (2022)

[2] M. Zoppello, M. Morandotti, H. Gadˆelha.
Controlling non-controllable scallops.
Submitted.

summer break
2022-05-23 13:40 - 15:10
by summer break as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Bangwei She (Inst. of Mathematics, Czech Academy of Sciences)
2022-03-21 14:40 - 16:10
Title: On convergence of numerical solutions for the compressible MHD system (https://master.researchseminars.org/talk/NSCM/68/)
by Bangwei She (Inst. of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Abstract
We study a general convergence theory for the analysis of numerical
solutions to a magnetohydrodynamic system describing the time
evolution of compressible, viscous, electrically conducting fluids.

First, we introduce the concept of consistent approximation mimicking
the density positivity, energy stability, and consistency of a
suitable numerical approximation. Further, we introduce the concept of
dissipative weak solution, which can be obtained as the weak limit of
the consistent approximation. Here, by “dissipative" we mean that
the energy inequality contains energy defects that control the
oscillations in the momentum equation.

Next, by using the relative energy functional, we prove the
dissipative weak-strong uniqueness principle, meaning that a
dissipative weak solution coincides with a classical solution of the
same problem as long as the latter exists. This indicates that a
consistent approximation converges unconditionally to the classical
solution. As a summary, we built a nonlinear variant of the Lax
equivalence theory for the compressible MHD system.

Finally, to show the application of the convergence theory, we propose
two numerical methods. We show that the numerical solutions preserve
the positivity of density and stability of the total energy. Then by
using the a priori estimates derived from the energy estimates we
prove that the numerical methods are consistent. Consequently, our
numerical methods belong to the class of consistent approximation.
Applying the prebuilt convergence theory, we conclude that the
solutions of our numerical methods converge to i) the dissipative
weak solution; ii) the classical solution as long as the classical
solution exists. As a byproduct of the first convergence, we prove the
global in-time existence of the dissipative weak solution.

Barbora Benešová (Charles University)
2022-04-25 13:40 - 15:10
Title: A model for polycrystalline Ni-Ti shape-memory alloys including plasticity (https://master.researchseminars.org/talk/NSCM/69/)
by Barbora Benešová (Charles University) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, I will discuss the interplay between the martensitic transformation and the plastic deformation in polycrystalline NiTi- alloys. I will then propose a phenomenological, macroscopic model capturing both effects within the generalized standard materials modelling framework. Special attention will be paid to distinguishing dependent and independent processes and their accurate modelling. This is a joint work with Miroslav Frost, Martin Kružík, Petr Sedlák and Hanuš Seiner.

Rufat Badal (University of Erlangen)
2022-02-14 14:40 - 16:10
Title: Nonlinear and Linearized Models in Thermoviscoelasticity (https://master.researchseminars.org/talk/NSCM/70/)
by Rufat Badal (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Abstract
We consider a quasistatic nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin’s-Voigt’s rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. The force balance is formulated in the reference configuration by resorting to the concept of nonsimple materials whereas the heat transfer equation is modeled by the Fourier law in the deformed configurations. Weak solutions are obtained by means of a staggered in-time discretization where the deformation and the temperature are updated alternatingly. Our result refines a recent work by Mielke & Roubíček [1] since our approximation does not require any regularization of the viscosity term. Afterwards, we focus on the case of deformations near the identity and small temperatures, and we show by a rigorous linearization procedure that weak solutions of the nonlinear system converge in a suitable sense to solutions of a system in linearized thermoviscoelasticity. The same property holds for time-discrete approximations and we provide a corresponding commutativity result.

[1] Mielke A., Roubíček T.: Thermoviscoelasticity in Kelvin-Voigt rheology at large strains. (2020)

Michele Ruggeri (University of Strathclyde)
2022-03-14 14:40 - 16:10
Title: The Landau-Lifshitz-Gilbert equation with Dzyaloshinki-Moriya interaction: numerical aspects (https://master.researchseminars.org/talk/NSCM/71/)
by Michele Ruggeri (University of Strathclyde) as part of Nečas Seminar on Continuum Mechanics

Abstract
The talk will be split into two parts.
In the first one, we discuss the numerical approximation of the Landau-Lifshitz-Gilbert equation
(LLG) for the case in which the energy (and, hence, the effective field appearing in LLG) includes
the Dzyaloshinki-Moriya interaction (DMI), the fundamental ingredient for the enucleation and stability
of chiral magnetic skyrmions. In the second part, we discuss a limiting model for micromagnetic thin
films in the presence of bulk DMI, where we focus on the limiting behavior of the magnetization
as the thickness of the film goes to zero. We show that the reduced model unveils some physics
and discuss its practical implications for computations. The results presented in the talk have been
obtained together with Giovanni Di Fratta (University of Naples Federico II), Elisa Davoli,
Carl-Martin Pfeiler, and Dirk Praetorius (TU Wien).

---
2022-04-11 13:40 - 15:10
by --- as part of Nečas Seminar on Continuum Mechanics

Abstract: TBA

Rita Ferreira (King Abdullah University of Science and Technology)
2022-10-31 14:40 - 16:10
Title: Structural changes in nonlocal denoising models arising through bi-level parameter learning (https://master.researchseminars.org/talk/NSCM/73/)
by Rita Ferreira (King Abdullah University of Science and Technology) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we will discuss a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a general topological space. Of particular interest is the non-compact parameter domains case, which is relevant, for instance, when the commonly used box constraints are disregarded. To overcome this lack of compactness, we propose a natural extension of the upper-level functional to the closure of the parameter domain via Gamma-convergence, which captures possible structural changes in the reconstruction model at the edge of the domain. Under two main assumptions, Mosco-convergence of the regularizers and uniqueness of minimizers of the lower-level problem, we prove that the extension coincides with the relaxation, thus admitting minimizers that relate to the parameter optimization problem of interest. To conclude, we apply this abstract framework to investigate four practically relevant models in image denoising, all featuring nonlocality; moreover, the associated families of regularizers exhibit qualitatively different parameter dependence, describing a weight factor, an amount of nonlocality, an integrability exponent, and a fractional order, respectively.
This talk is based on a joint work with Elisa Davoli, Carolin Kreisbeck, and Hidde Schönberger.

Lennart Machill (University of Muenster, Germany)
2022-10-10 13:40 - 15:10
Title: One-dimensional viscoelastic von Kármán theories (https://master.researchseminars.org/talk/NSCM/74/)
by Lennart Machill (University of Muenster, Germany) as part of Nečas Seminar on Continuum Mechanics

Abstract
We derive an effective one-dimensional limit from a three-dimensional Kelvin-Voigt model for viscoelastic thin-walled beams, in which the elastic and the viscous stress tensor comply with a frame-indifference principle. The limiting system of equations comprises stretching, bending, and twisting both in the elastic and the viscous stress. It coincides with the model already identified via [Friedrich-Kružík '20] and [Friedrich-Machill '22] by a successive dimension reduction, first from 3D to a 2D theory for von Kármán plates and then from 2D to a 1D theory for ribbons. Our arguments rely on the static Gamma-convergence in [Freddi-Mora-Paroni '13], on the abstract theory of metric gradient flows, and on evolutionary Gamma-convergence by Sandier and Serfaty.

Elvira Zappale (University of Rome - I, Sapienza)
2022-11-21 14:40 - 16:10
Title: Variational formulation for hierarchies of structured deformations (https://master.researchseminars.org/talk/NSCM/75/)
by Elvira Zappale (University of Rome - I, Sapienza) as part of Nečas Seminar on Continuum Mechanics

Abstract
The mechanical theory of first order structured deformations formulated in [2] enriches the purely macroscopic field theory of non-linear elasticity by taking into account the effects of disarrangements that occur at a single submacroscopic level. In [1] a variational formulation for this theory has been successfully provided in the context of special fields of bounded variation.
Taking into account that many natural and man-made physical systems have a rich enough geometrical structure to permit the identification of hierarchies consisting of more than one physically meaningful submacroscopic level, the mechanical theory of structured deformations has been enriched in [3]. This talk aims at presenting a variational framework of these latter theoretical settings.

References:

[1] R. Choksi and I. Fonseca: Bulk and interfacial energy densities for structured deformations of continua. Arch. Rational Mech. Anal. 138 (1997), 37-103.

[2] G. Del Piero and D. -R. Owen: Structured deformations of continua: Arch. Ration. Mech. Anal. 124 (1993), 99-155.

[3] L. Deseri and D. R. Owen: Elasticity with Hierarchical Disarrangements: A Field Theory That Admits Slips and Separations at Multiple Submacroscopic Levels: J.of Elasticity Vol- 135 (2019) Issue 1-2, 149-180.

Joint project with Ana Cristina Barroso, José Matias, Marco Morandotti & David Owen

Martin Horák (Faculty of Civil Engineering, CTU, ÚTIA AVČR)
2022-10-03 13:40 - 15:10
Title: Efficient formulation of a two-dimensional geometrically exact Bernoulli beam (https://master.researchseminars.org/talk/NSCM/76/)
by Martin Horák (Faculty of Civil Engineering, CTU, ÚTIA AVČR) as part of Nečas Seminar on Continuum Mechanics

Lecture held in K3 Karlin, Sokolovska 83, Praha 8.

Abstract
In this talk, I will focus on a two-dimensional geometrically exact formulation of a Bernoulli beam.
The formulation is based on the integrated form of equilibrium equations, which are combined with the
kinematic equations and generalized material equations, leading to a set of three first-order differential
equations. These equations are then discretized by finite differences and the boundary value problem is
converted into an initial value problem using a technique inspired by the shooting method. The accuracy of
the numerical approximation is conveniently increased by refining the integration scheme on the element
level while the number of global degrees of freedom is kept constant, which leads to high computational
efficiency. The element has been implemented into an open-source finite element code. I will show a
favorable comparison with standard beam elements formulated in the finite-strain framework and with
analytical solutions. Several extensions of the proposed approach, including curved initial geometry, follower pressure load, and beam-to-beam contact will be also discussed. This is joint work with M. Jirásek and E. La Malfa Ribolla.

REFERENCES

[1] Jirásek, M.,La Malfa Ribolla, E., and Horák, M. Efficient finite difference formulation of a ge-ometrically nonlinear beam element. International Journal for Numerical Methods in Engineering,(2021) 122:7013–7053.

[2] Horák, M., La Malfa Ribolla, E., and Jirásek, M. Efficient formulation of a two-noded geometrically exact curved beam element. International Journal for Numerical Methods in Engineering, (2022), accepted for publication.

Bohumír Bastl (University of West Bohemia)
2022-10-24 13:40 - 15:10
Title: Numerical simulation of incompressible fluid flow with the help of isogeometric analysis (https://master.researchseminars.org/talk/NSCM/77/)
by Bohumír Bastl (University of West Bohemia) as part of Nečas Seminar on Continuum Mechanics

Abstract
Isogeometric analysis is a relatively recently introduced concept for numerical
solving of partial differential equations which bridges the gap between
geometric modelling and numerical simulation/analysis.

In this talk, the isogeometric analysis is used for numerical simulation of
incompressible fluid flow. We give an overview of the method which shares many
features with Finite Element Method, but different meshes and basis functions
also lead to significant differences. We present advantages and drawbacks of the
method which we have encountered during development of incompressible turbulent
flow solver and we focus on our results concerning isogeometric mesh generation,
stabilization methods and solving systems of linear equations in this context.

John Simon (Institute of Mathematics, Czech Academy of Sciences)
2022-11-14 14:40 - 16:10
Title: A NAIVE FORMULATION OF MAXIMIZING THE COMPUTATIONAL CAPABILITY OF THE TWIN VORTEX COMPUTER VIA SHAPE OPTIMIZATION (https://master.researchseminars.org/talk/NSCM/78/)
by John Simon (Institute of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Physical reservoir computing is a new computational paradigm based on recurrent neural networks
where instead of optimizing nodal connection of the internal network, one gets to utilize the nonlinear behavior of
physical systems and gets to focus on optimizing a minimal number parameters. In 2021, Goto et al [1] investigated
a physical reservoir computer in the context of a flow past a cylinder and shown that the computer’s computational
capability is maximized at the bifurcation point between the generation of twin vortex and the onset of Karman vortex.
In this exposition, the authors illustrated how the the dynamics of twin vortex affects the ability of the computer to
accomplish certain tasks. In particular, they have shown that the length of the twin vortex is directly proportional to
the performance.
In this talk, a shape optimization problem that aims to increase the said capability will be presented. The op-
timization problem is a naive formulation by maximizing two types of functional which has been historically used a
quantifiers of vortex, namely, the L2-norm of the curl of the velocity and the positivity of the determinant of the velocity
gradient. The optimization problem is regularized by a perimeter functional which acts as a Tikhonov regularizer. A
volume constraint is also imposed, which — together with the regularizer — prevents possible topological changes in
the domain. The analysis of this problem includes existence analysis of the governing state, establishing the existence
of shape solutions, and sensitivity of the objective functional with respect to domain perturbation. We shall then utilize
the results of the sensitivity analysis to a gradient descent-type algorithm for numerical illustrations.

[1] K. Goto, K. Nakajima, and H. Notsu, Twin vortex computer in fluid flow, New J. Phys., 23 (2021), p. 063051,
https://doi.org/doi.org/10.1088/1367-2630/ac024d.

Jiří Mikyška (Faculty of Nuclear Sciences and Physical Engineering, Czech Tech. University)
2022-10-17 13:40 - 15:10
Title: An alternative model of multicomponent diffusion based on a combination of the Maxwell-Stefan theory and continuum mechanics. (https://master.researchseminars.org/talk/NSCM/79/)
by Jiří Mikyška (Faculty of Nuclear Sciences and Physical Engineering, Czech Tech. University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
I will present a theory of multicomponent mixtures that do not employ any splitting of component fluxes
into convective and diffusive parts. Instead, momentum balance is formulated individually for each
component in which both 1) viscous friction within a component, and 2) momentum exchange among different
components, are taken into account. While viscous friction is described using the Newtonian stress
tensor, the Maxwell-Stefan theory is used to describe the momentum exchange among different components.
When the viscosity is neglected, the model of an ideal mixture of ideal gases leads to a hyperbolic system of
conservation laws. For the non-ideal mixtures, we obtain the first-order system in a non-conservative form.
A simplified version of the model is discretized using a combination of the finite volume method and the
mixed-hybrid finite element method. Numerical examples are provided to show the typical behavior of the
solution of the model equations.

Dallas Albritton (Princeton University)
2022-12-05 14:40 - 15:10
Title: Non-uniqueness of Leray solutions to the forced Navier-Stokes equations (https://master.researchseminars.org/talk/NSCM/80/)
by Dallas Albritton (Princeton University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Institute of Mathematics, Žitná 25, Praha 1, library.

Abstract
In a seminal work, Leray demonstrated the existence of
global weak solutions to the Navier-Stokes equations in three
dimensions. Are Leray's solutions unique? This is a fundamental
question in mathematical hydrodynamics, which we answer in the
negative within the `forced' category, by exhibiting two distinct
Leray solutions with zero initial velocity and identical body force.

This is joint work with Elia Brué and Maria Colombo.

semester break
2023-01-09 14:40 - 16:10, 2023-01-16 14:40 - 16:10, 2023-01-23 14:40 - 16:10, 2023-01-30 14:40 - 16:10, 2023-02-06 14:40 - 16:10, 2026-01-12 14:40 - 16:10, 2026-01-19 14:40 - 16:10, 2026-01-26 14:40 - 16:10 and 2 more dates
by semester break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Cy Maor (Hebrew University of Jerusalem)
2023-03-20 14:40 - 16:10
Title: Non-Euclidean elasticity: shape transitions in non-Euclidean ribbons (https://master.researchseminars.org/talk/NSCM/86/)
by Cy Maor (Hebrew University of Jerusalem) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Many bodies in nature that undergo inhomogeneous growth/shrinkage become "pre-strained"; that is, they are stressed even in the absence of external forces. They are typically modeled by having an intrinsic non-flat metric, giving rise to non-Euclidean elasticity.
Of particular interest are thin bodies: shell-like, rod-like or ribbon-like bodies (e.g., leaves or supramolecular assemblies), which exhibit interesting energy-driven patterns. In this talk I will describe the model of non-Euclidean elasticity, and then focus on thin bodies, the relations between their intrinsic curvature and their elastic behavior, and specifically on shape transitions in non-Euclidean ribbons.

Easter Monday
2023-04-10 13:40 - 15:10, 2026-04-06 13:40 - 15:10
by Easter Monday as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Holiday
2023-05-01 13:40 - 15:10, 2023-05-08 13:40 - 15:10
by Holiday as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Petr Sváček (Faculty of Mechanical Engineering, CTU)
2023-05-22 13:40 - 15:10
Title: On Application of Finite Element Method for Fluid-Structure-Acoustic Interactions Related to Human Phonation Process (https://master.researchseminars.org/talk/NSCM/90/)
by Petr Sváček (Faculty of Mechanical Engineering, CTU) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Human voice is created by a complex process consisting of mutual
interactions of flowing air, vibrating vocal folds and the sound propagation
through the vocal tract. The fundamental sound is created by the mutual
interaction of the flowing air with vibrations of vocal folds(VFs). The
arising fundamental sound is enriched by aeroacoustic sound sources and
propagated through the vocal tract. In this talk, mathematical models of a
simplified fluid-structure-acoustic interaction problem shall be,
numerically discretized and numerical results will be presented. In
particular the deformation of an elastic body representing the model of
vocal folds will be considered in the interaction with the complex fluid
flow and aeroacoustics. In particular the attention will be paid to several
important issues of such a modelling as the inclusion of the VFs contact,
choice of suitable boundary conditions, the influence of pre-stressed vocal
fold on the fundamental frequency, etc. For the flow model the realization
of the variational multiscale method is discussed. The numerical
approximation of the problem is presented and numerical results are shown.

Xmas
2022-12-26 14:40 - 16:10
Title: no talk (https://master.researchseminars.org/talk/NSCM/91/)
by Xmas as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Gabriel Pathó (Dlubal Software CS)
2022-11-07 14:40 - 16:10
Title: Constitutive modelling of masonry for civil engineering (https://master.researchseminars.org/talk/NSCM/92/)
by Gabriel Pathó (Dlubal Software CS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We discuss the macroscale modeling of masonry consisting of brick and mortar as a brittle material and its implementation in the commercial software RFEM 6 which is convenient for practical civil engineers and complies with both Eurocode 6 and available test data.

cancelled
2022-11-28 14:40 - 16:10
Title: seminar is cancelled (https://master.researchseminars.org/talk/NSCM/93/)
by cancelled as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Michael Růžička (University of Freiburg)
2022-12-05 16:10 - 17:10
Title: Existence proofs for pseudomonotone parabolic problems (https://master.researchseminars.org/talk/NSCM/94/)
by Michael Růžička (University of Freiburg) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Institute of Mathematics, Žitná 25, Praha 1, library.

Abstract
In the talk we discuss nonlinear parabolic problems which
contain a pseudomonotone operator. A new notion of Bochner pseudomonotonicity is introduced and
applied. Extensions to quasi non-conforming and non-conforming Bochner pseudomonotonicity yield
convergence proofs for fully discrete Rothe–Galerkin schemes in the framework of discretely divergence free FE and DG methods.

References
[1] E. Baumle and M. Růžička: Note on the existence theory for evolution
equations with pseudomonotone operators, Ric. Mat., 2017.

[2] S. Bartels, M. Růžička: Convergence of fully discrete implicit and
semi-implicit approximations of singular parabolic equations, SIAM J. Numer. Anal., 2020.

[3] A. Kaltenbach, M. Růžička: Note on the existence theory for
pseudo-monotone evolution problems, J. Evol. Equ., 2021.

[4] L.C. Berselli, A. Kaltenbach, M. Růžička: Analysis of fully
discrete, quasi non-conforming approximations of evolution equations and applications, Math. Models
Methods Appl. Sci., 2021.

[5] A. Kaltenbach, M. Růžička: Analysis of fully discrete, non-conforming approximation of evolution equations and applications, in preparation, 2022.

Sourav Mitra (Institute of Mathematics, Czech Academy of Sciences)
2022-12-12 14:40 - 16:10
Title: Existence of a weak solution for a compressible multicomponent fluid-structure interaction problem (https://master.researchseminars.org/talk/NSCM/95/)
by Sourav Mitra (Institute of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
I will speak about our recent work on the analysis of a system of PDEs governing the interaction between two compressible mutually noninteracting fluids and a shell of Koiter type encompassing a time-dependent 3D domain filled by the fluids. The dynamics of the fluids is modeled by compressible
Navier-Stokes equations with a physically realistic pressure depending on the densities of both fluids. The shell constitutes the boundary of the fluid domain, and it possesses a non-linear, non-convex Koiter energy (of a quite general form). We are interested in the existence of a weak solution to the system
until the time-dependent boundary approaches a self-intersection. We first prove a global existence result (until a degeneracy occurs) when the adiabatic exponents solve max{γ, β} > 2 and min{γ, β} > 0, and further, the densities are comparable. Next, with a slightly extra regularity assumption on the
initial structural displacement, we extend our global existence result to the case max{γ, β} ≥ 2 and min{γ, β} > 0.
In the first part of the talk, I will try to introduce the classical theory on the existence of weak solutions for compressible mono-fluid models. Next, I will talk about our work on the multi-component FSI problem. This is joint work with M. Kalousek and Š. Nečasová.

Nilasis Chaudhuri (Imperial College London)
2022-12-19 14:40 - 16:10
Title: Navier--Stokes--Fourier system with Dirichlet boundary conditions for temperature (https://master.researchseminars.org/talk/NSCM/96/)
by Nilasis Chaudhuri (Imperial College London) as part of Nečas Seminar on Continuum Mechanics

Abstract
In this talk, we consider the Navier--Stokes--Fourier system,
describing the motion of a compressible, viscous, and heat conducting
fluid in a bounded domain $\Omega \subset R^d$, $d =2,3$, with general
non-homogeneous Dirichlet boundary conditions for the absolute
temperature. We introduce a new concept of weak solution based on the
satisfaction of the entropy inequality together with a balance law for
the ballistic energy. We show the existence of global-in-time weak
solutions, as well as the weak--strong uniqueness principle.

Jiří Outrata (Czech Academy of Sciences, Institute of Information Theory and Automation)
2023-01-02 14:40 - 16:10
Title: On the application of the SCD semismooth* Newton method to variational inequalities of the second kind (https://master.researchseminars.org/talk/NSCM/97/)
by Jiří Outrata (Czech Academy of Sciences, Institute of Information Theory and Automation) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The first part of the lecture deals with a description of the SCD (subspace containing
derivative) mappings and the SCD semismooth* Newton method for the solution of general
inclusions. This method is then applied to a class of variational inequalities of the second
kind. As a result, one obtains an implementable algorithm exhibiting a locally superlinear
convergence. Finally, we demonstrate the efficiency of a globalized version of this method
via a Cournot-Nash equilibrium in which the objectives of the players (firms) are nonsmooth
due to the presence of the so-called cost of change. The problem is modeled as a variational
inequality of the second kind and, to test the performance of the applied method, one admits
really large numbers of players and produced commodities.
Joint work with: Helmut Gfrerer and Jan Valdman.

Malte Kampschulte (Faculty of Mathematics and Physics, Charles University)
2023-02-13 14:40 - 16:10
Title: Self-contact for inertial problems in continuum mechanics (https://master.researchseminars.org/talk/NSCM/98/)
by Malte Kampschulte (Faculty of Mathematics and Physics, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
There are many theories about elastic collisions of solids and the resulting inertial evolution. What unifies most of them is that they involve some phenomenological assumption. The aim of this talk is to present a recent result which shows that for the self-collision of elastic bulk solids, it is in fact sufficient to consider matter non-interpenetration. Based only on this, we are able to derive existence of weak solutions including contact with obstacles and self-contact for arbitrary large times and for large deformations. Additionally we are able to precisely characterize the contact forces as a vector-valued measure. This is based on joint works with A. Češík, and G. Gravina.

Ivan Gudoshnikov (Institute of Mathematics, Czech Academy of Sciences)
2023-02-20 14:40 - 16:10
Title: Elastoplasticity with softening in spring network models: a state-dependent sweeping process approach (https://master.researchseminars.org/talk/NSCM/99/)
by Ivan Gudoshnikov (Institute of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Softening plasticity and Gurson model of damage in particular lead to ill-posed mathematical
problems due to the loss of monotonicity. Multiple co-existing solutions are possible when softening
elements are coupled together, and solutions cannot be continued beyond the point of complete
failure of a material. Moreover, spatially continuous models with softening suffer from localization
of strains and stresses to measure-zero submanifolds.
We formulate a problem of quasistatic evolution of elasto-plastic spring networks (Lattice Spring
Models) with a plastic flow rule which describes linear hardening, linear softening and perfectly
plastic springs in a uniform manner. The fundamental kinematic and static characteristics of the
network are described by the rigidity theory and structural mechanics.
To solve the evolution problem we convert it to a type of a differential quasi-variational inequality known as the state-dependent sweeping process. We prove the existence of solution to the
associated time-stepping problem (implicit catch-up algorithm), and the estimates we obtain imply
the existence of a solution to the (time-continuous) sweeping process.
Using numerical simulations of regular grid-shaped networks with softening we demonstrate
the development of non-symmetric shear bands. At the same time, in toy examples it is easy to
analytically derive multiple co-existing solutions, appearing in a bifurcation which happens when
the parameters of the networks continuously change from hardening through perfect plasticity to
softening.

Pei Su (Charles University, Faculty of Mathematics and Physics)
2023-02-27 14:40 - 16:10
Title: Asymptotic analysis of the system describing a small moving rigid body in viscous incompressible fluid (https://master.researchseminars.org/talk/NSCM/100/)
by Pei Su (Charles University, Faculty of Mathematics and Physics) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We consider the interaction between a viscous incompressible fluid and a
small rigid body, which is immersed in the fluid. The fluid is modeled by
the 3D Navier-Stokes equations. The motion of the body obeys the conservation of linear and angular momentum. We assume that the density of the
body is constant which is independent of the size of the body ε. Based on
the L
p − L
q
estimate of the so-called fluid-structure semigroup, we obtain a
uniform estimate for the velocity of the body. In particular, we show that
these estimates are ε-invariant. This help us to construct an approximation
sequence of the test functions of the fluid-body system. We prove that the solution of the fluid-body system, in appropriate sense, converges to a solution
of the Navier-Stokes equations as ε → 0.
This is a joint work with Jiao He (Univerist´e Paris-Sud).

Edoardo Mainini (University of Genoa)
2023-03-06 14:40 - 16:10
Title: Stability conditions for the linearization of pure traction problems of finite elasticity. (https://master.researchseminars.org/talk/NSCM/101/)
by Edoardo Mainini (University of Genoa) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We discuss the linearization of finite elasticity by means of Gamma-convergence for the case of pure traction problems. For hyperelastic bodies subject to equilibrated force fields, the limit energy can be different from the global energy of linear elasticity subject to the same force field. However, under a suitable curl constraint, we show that the linear elastic equilibrium can be obtained as limit of local minimizers of finite elasticity. This is joint work with Roberto Ognibene and Danilo Percivale.

Monika Balaszová (Facaulty of Mathematics and Physics, Charles University)
2023-05-15 13:40 - 15:10
Title: Discontinuous Galerkin method for problems in time-depend domains – theory and applications (https://master.researchseminars.org/talk/NSCM/102/)
by Monika Balaszová (Facaulty of Mathematics and Physics, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Most of the theoretical mathematical results on the solvability and numerical analysis of nonstationary partial differential equations are obtained under the assumption that a space domain is independent of time. However, problems in time-dependent domains are important in a number of areas of science and technology. This is particularly the case of fluid-structure interaction problems, when the flow is solved in a domain deformed due to the coupling with an elastic structure. There are various approaches to the solution of problems in time-dependent domains, a very popular technique is the arbitrary Lagrangian-Eulerian (ALE) method. In this talk we present an ALE version of the space-time discontinuous Galerkin method, which is based on piecewise polynomial approximations over finite element meshes, in general discontinuous on interfaces between neighbouring elements. We show that the proposed method is numerically unconditionally stable and demonstrate its robustness on a numerical solution of the nonlinear elasticity benchmark problem. The developed method is also applied to the numerical simulation of air flow in a simplified model of human vocal tract and flow induced vocal folds vibrations.

Florian Oschmann (Institute of Mathematics AS CR)
2023-03-13 14:40 - 16:10
Title: Some insides in homogenization of compressible Navier-Stokes equations (https://master.researchseminars.org/talk/NSCM/103/)
by Florian Oschmann (Institute of Mathematics AS CR) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We investigate the homogenization of the two- and
three-dimensional unsteady compressible Navier-Stokes equations, and
show (i) the convergence result for the 2D case, and (ii) a better lower
bound for the adiabatic exponent occurring in the pressure law for the
3D case. The latter will be covered with two different proofs. Lastly,
we briefly discuss the optimality of the achieved bounds for the
adiabatic exponent in terms of the underlying space-time dimension. This
is joint work with Šárka Nečasová (CAS) and Milan Pokorný
(Charles University).

Marco Morandotti (Politecnico di Torino)
2023-04-03 13:40 - 15:10
Title: Semi-discrete modeling of systems of disclinations and dislocations (https://master.researchseminars.org/talk/NSCM/104/)
by Marco Morandotti (Politecnico di Torino) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Disclinations in crystalline materials are point defects that are responsible for rotational kinematic incompatibility. They are characterised by the so-called Frank angle, measuring the severity of the lattice mismatch. In a two-dimensional medium under the assumption of plain strain, the Airy stress function can be used to translate the measure of incompatibility into a fourth-order PDE with measure data.

We propose a variational model for disclinations in two-dimensional materials by means of the core-radius approach. Moreover, we identify a good scaling regime in which we study the effective behaviour of dipoles of disclinations (of opposite signs), thus validating analytically the results obtained in [Eshelby, 1966]: a dipole of plane disclinations generates an edge dislocation with Burgers vector perpendicular to the dipole axis. Finally, we study the energy of a system of a finite number of dipoles of disclinations and recover the results of [Cermelli-Leoni, 2005] for edge dislocations.

This is work in collaboration with Pierluigi Cesana (Kyushu University) and Lucia De Luca (CNR Rome).

Franco Tomarelli (Politecnico di Milano)
2023-04-24 13:40 - 15:10
Title: Pure traction and Signorini problem between linear and finite elasticity (https://master.researchseminars.org/talk/NSCM/105/)
by Franco Tomarelli (Politecnico di Milano) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
A limit elastic energy for pure traction problem is derived from re-scaled nonlinear energies of a
hyper-elastic material body subject to an equilibrated force field.
We show that the strains of minimizing sequences associated to re-scaled nonlinear energies weakly
converge, up to subsequences, to the strains of minimizers of a limit energy.
The limit energy functional exhibits a gap that makes it different from the classical linear elasticity
functional. Nevertheless a suitable compatibility condition entails the coincidence of related minima
and minimizers, hence the rigorous validation of linear elasticity. Strong violation of this condition
provides a limit energy which is unbounded from below, while a mild violation may produce
unboundedness of strains and a limit energy which has infinitely many extra minimizers which are
not minimizers of standard linear elastic energy. As a consequence, a rigorous validation of linear
elasticity fails for compressive force fields that infringe such a compatibility condition.
This phenomenon has relevant consequences also on the validation of the Signorini problem in
linear elasticity: there are loads pushing the body against the obstacle, but unfit for the geometry of
the whole system body-obstacle, so that the corresponding variational limit turns out to be different
from the classical Signorini problem. However, if the force field acting on the body fulfils an
appropriate geometric admissibility condition, we can show coincidence of related solutions.
The asymptotic analysis provides a sharp and rigorous variational justification of the unilateral
problem in linear elasticity, together with an accurate analysis of the unilateral constraint.
These results were obtained in a joint research with Francesco Maddalena (Politecnico di Bari) and
Danilo Percivale (Università di Genova).

Manuel Friedrich (University of Erlangen)
2023-03-27 13:40 - 15:10
Title: Finite crystallization via stratification (https://master.researchseminars.org/talk/NSCM/106/)
by Manuel Friedrich (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In this talk, I present a new technique to prove two-dimensional
crystallization results in the square lattice for finite particle
systems. We consider configurational energies featuring two-body
short-ranged particle interactions and three-body angular potentials
favoring bond-angles of the square lattice. To each configuration, we
associate its bond graph which is then suitably modified by identifying
chains of successive atoms. This method, called stratification, reduces
the crystallization problem to a simple minimization that corresponds to
a proof via slicing of the isoperimetric inequality in l1. Based on
joint work with Leonard Kreutz.

Katerina Nik (University of Vienna)
2023-04-17 13:40 - 15:10
Title: Analysis of a three-dimensional model for MEMS with a hinged upper plate (https://master.researchseminars.org/talk/NSCM/107/)
by Katerina Nik (University of Vienna) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
An idealized electrostatic microelectromechanical system (MEMS) consists of a rigid ground plate above which a thin elastic plate is suspended. The elastic plate is assumed to be hinged on its boundary. Applying a voltage difference between the two plates induces a Coulomb force that deforms the elastic plate. The corresponding mathematical model couples a fourth-order parabolic equation for the vertical deformation of the elastic plate to the harmonic electrostatic potential in the free domain between the two plates. In this talk, I will present some recent results on local and global well-posedness of the model as well as on existence and non-existence of stationary solutions.

Semester break
2023-05-29 13:40 - 15:10
Title: We'll go on in October 2023 (https://master.researchseminars.org/talk/NSCM/108/)
by Semester break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

semestr break
2023-09-04 13:40 - 15:10, 2023-09-11 13:40 - 15:10, 2023-09-18 13:40 - 15:10, 2023-09-25 13:40 - 15:10
by semestr break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Angkana Rüland (University of Bonn)
2023-10-02 13:40 - 15:10
Title: Rigidity and Flexibility in the Modelling of Shape-Memory Alloys (https://master.researchseminars.org/talk/NSCM/113/)
by Angkana Rüland (University of Bonn) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In the modelling of shape-memory alloys, a striking dichotomy between rigid and flexible behaviour emerges: On the one hand, in many physically relevant settings, exactly stress-free structures of sufficiently high regularity can be shown to satisfy the kinematic compatibility conditions given by the characteristics of the compatibility equations. The solutions are rigid. On the other hand, when dropping these regularity conditions, the method of convex integration shows that a plethora of wild, irregular solutions exist which do not satisfy the kinematic conditions in general. These solutions can approximate a large class of boundary data and are thus flexible. In this talk, I discuss an approach towards investigating this dichotomy in more detail based on scaling laws. For a class of simplified models, we show that the complexity of the microstructure is captured by these scaling laws both in settings with displacement and with nucleation boundary conditions.

The talk is based on joint work with P. Cesana, F. Della Porta, J. M. Taylor, A. Tribuzio, Ch. Zillinger, B. Zwicknagl.

Illia Donhauzer (La Trobe University)
2023-10-09 13:40 - 15:10
Title: Limit theorems for multifractal products of random fields (https://master.researchseminars.org/talk/NSCM/114/)
by Illia Donhauzer (La Trobe University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The talk is about random functions with changing local regularity
exponent (multifractal processes and multifractal fields in multidimensional
cases). This type of random function has been observed in various areas
including communication systems, precipitation fields, econometrics, and so
on. The goal of this talk is to present new results in the modeling of
multifractal random functions. One of the possible approaches to obtain
multifractal random functions is as limits of multifractal products of
random functions (roughly speaking, integrals of infinite products of random
functions). In the talk, I will show new results on the existence of those
limits in the spaces Lq as well as new results on the rate of convergence.
The developed methodology is also applied to multidimensional multifractal
measures. Finally, I will show a new class of examples of geometric
φ-sub-Gaussian random functions when the general assumptions have a simple
form and can be expressed in terms of covariance functions only.

Kerrek Stinson (University of Bonn)
2024-01-08 14:40 - 16:10
Title: Regularity for minimizers of the Griffith fracture energy (https://master.researchseminars.org/talk/NSCM/115/)
by Kerrek Stinson (University of Bonn) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The Griffith criterion says that the energy to crack a brittle
elastic material is proportional to the length of the crack. Understanding
the regularity of minimizers requires unraveling the complex interplay of
bulk (elastic) and surface (crack) energies in the vectorial setting of
linearized frame indifference. In dimension 2, we prove that the crack of a
minimizer is given by a $C^{1,\alpha}$ surface outside of a singular set of
points that has dimension strictly less than 1, analogous to results for the
scalar Mumford-Shah functional. Joint work with Manuel Friedrich (FAU) and
Camille Labourie (UPS).

Valentin Calisti (Institute of Mathematics, Czech Academy of Sciences)
2023-10-30 14:40 - 16:10
Title: Minimization of blood damage induced by non-Newtonian fluid flows in moving domains (https://master.researchseminars.org/talk/NSCM/116/)
by Valentin Calisti (Institute of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Many engineering works are interested in the parametric optimization of
blood pumps to minimize hemolysis (destruction of red blood cells).
In order to generalize this approach, we study the shape continuity of a
coupled system of PDEs modeling blood flows and hemolysis evolution in
moving domains, governed respectively by generalized Navier-Stokes and
transport equations.

First, the shape continuity of the blood flow solutions is shown. This
development, which extends the one led in (Sokolowski, Stebel, Evol.
Equ. Control Theory, 2014) to the case of shear thinning fluids, is
based on the recent progress made in (Nägele, Ružička, J. Differential
Equations, 2018), adapted to the present framework of a sequence of
converging moving domains.

After calculating blood flows solutions, the velocity and stress fields
are used as coefficients and r.h.s for the transport equation governing
the evolution of the hemolysis rate. From this, the shape continuity of
the hemolysis rate is also proved.

Finally, these results allow to show the existence of minimum for a
class of shape optimization problems based on the minimization of the
hemolysis rate, in the framework of moving domains.

CANCELLED
2023-12-11 14:40 - 16:10
by CANCELLED as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We discuss the stability of objective structures of interacting atoms that form a far-reaching generalization of crystal lattices. To this end, we use methods from harmonic analysis to set up a second derivative test of the configurational energy at equilibria, a key point being the identification of a carefully chosen seminorm with respect to which coercivity is estimated. In particular, a novel discrete Korn-type inequality is established in the setting of objective structures. We also provide an efficient algorithm to check for atomistic stability, which we illustrate numerically for a general carbon nanotube. (This is joint work with M. Steinbach, Augsburg).

Anastasia Molchanova (University of Vienna)
2023-12-04 14:40 - 16:10
Title: Variational Model of a Hyperelastic Capacitor (https://master.researchseminars.org/talk/NSCM/118/)
by Anastasia Molchanova (University of Vienna) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
This talk discusses an interplay between elastic deformations and electrostatic capacitance for charged elastic materials. We consider a variational model, where electroelastic energy involves coupling elastic response and electrostatics using a capacitary term naturally defined in Eulerian coordinates. The ensuing electroelastic energy is then of mixed Lagrangian-Eulerian type. We study the continuity properties of the capacitary terms under the convergence of the deformations and prove the existence of minimizers.

Jiří Zeman (Faculty of Mathematics and Physics, Charles University)
2023-11-06 14:40 - 16:10
Title: Bending-torsion theories for elastic and brittle nanowires as Gamma-limits of atomistic models (https://master.researchseminars.org/talk/NSCM/119/)
by Jiří Zeman (Faculty of Mathematics and Physics, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Nanotechnology has ranked among paradigm-shifting and the fastest growing research areas over the last 30 years. To benefit from the wide application prospects of engineered nanoworld objects, it is important to study their mechanical response, which often differs from that of macroscopic bodies, though (because of size or structure effects for example). In particular, there exist rod-like structures in nanoengineering which are long enough in one direction for continuum theories to be applicable, but in the perpendicular direction, they have a diameter on the scale of tens to hundreds of atoms. In this talk, derivation of nonlinear continuum models for thin and ultrathin rods will be presented. We start from a 3D crystalline lattice with short-range interactions and study simultaneous limits of vanishing rod thickness and interatomic distance. Gamma-convergence especially yields a novel theory for inextensible rods that undergo bending, torsion, and brittle fracture. New discrete and surface terms appear in the limiting energy functional, whose fracture part is expressed by an implicit cell formula that covers different modes of fracture, including (complete) cracks, folds and torsional cracks. Joint work with Bernd Schmidt (Augsburg).

Stefano Almi (University of Naples)
2023-11-27 14:40 - 16:10
Title: Strain gradient plasticity and multi-well potentials (https://master.researchseminars.org/talk/NSCM/120/)
by Stefano Almi (University of Naples) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
I will present a strain-gradient plasticity model obtained as
$\Gamma$-limit of a nonlinear finite dislocation model characterised by
a multiple-well potential and a singular perturbation term accounting
for the divergence of the strain field. The analysis builds upon a new
quantitative rigidity estimate for incompatible fields in presence of a
multiwell elastic energy, showing that the $L^{1^{*}}$-distance of a
strain field from a single well is controlled in terms of the
$L^{1^{*}}$-distance from a finite set of wells, of curl $\beta$, and
of ${\rm div} \beta$. This is a joint work with Dario Reggiani (Scuola
Superiore Meridionale) and Francesco Solombrino (University of Naples
Federico II).

Xmas
2023-12-25 14:40 - 16:10, 2023-12-18 14:40 - 16:10
by Xmas as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Raffaele Grande (Czech Academy of Sciences, Institute of Information Theory and Automation)
2023-10-23 13:40 - 15:10
Title: Stochastic control problems and a convergence result for horizontal mean curvature flow (https://master.researchseminars.org/talk/NSCM/122/)
by Raffaele Grande (Czech Academy of Sciences, Institute of Information Theory and Automation) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The evolution by horizontal mean curvature flow was broadly studied for its applications in neurogeometry and in image processing (e.g. Citti-Sarti model). It represents the contracting evolution of a hypersurface embedded in a particular geometrical setting, called sub-Riemannian geometry, in which only some curves (called horizontal curves) are admissible by definition. This may lead to the existence of some points of the hypersurface, called characteristic, in which is not possible to define the so-called horizontal normal. To avoid this problem, it is possible to use the notion of Riemannian approximation of a sub-Riemannian geometry applied to the horizontal mean curvature flow.

I will show the connection between the evolution of a generic hypersurface in this setting and the associated stochastic optimal control problem. Then, I will show some results of asymptotic optimal controls in the Heisenberg group and use them to show later a convergence result between the solutions of the approximated mean curvature flow and the horizontal ones. This is from some joint works with N. Dirr and F. Dragoni.

Tomáš Bodnár (Faculty of Mechanical Engineering, Czech Technical University)
2023-10-16 13:40 - 15:10
Title: On the estimation of blood hemolysis index from viscoelastic stretch model (https://master.researchseminars.org/talk/NSCM/123/)
by Tomáš Bodnár (Faculty of Mechanical Engineering, Czech Technical University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
This contribution presents an alternative way of estimating the blood damage
hemolysis index using the viscoelastic stretch tensor. This tensor is obtained
by solving a set of coupled partial differential equations describing the
rheology of shear-thinning viscoelastic fluid. The main advantage of the chosen
approach is that the already calculated and known stretch tensor is just reused
and postprocessed to assess the local deformation of red blood cells, that can
in certain cases lead to degradation of the cell membranes and consequent
release of hemoglobin. The algorithm of solving the viscoelastic stretch tensor
equations and hemolysis index postprocessing will be outlined and discussed in
detail. Some initial numerical simulations for an axisymmetric idealized
stenosed blood vessel, obtained using an in-house finite-volume solver, will be
presented.

Marco Bresciani (Department of Mathematics, University of Erlangen)
2023-11-13 14:40 - 16:10
Title: CANCELED (https://master.researchseminars.org/talk/NSCM/124/)
by Marco Bresciani (Department of Mathematics, University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We study a variational model for ferromagnetic elastomers featuring a mixed Eulerian-Lagrangian formulation. The magnetic variable is defined on the deformed configuration
in the actual space and the saturation constraint involves the Jacobian determinant of
deformations.
First, in the case for purely elastic materials, we discuss the existence of equilibrium
configurations and we investigate the model under quasistatic evolution in the rate-independent setting. Subsequently, we address the extension of the existence theory for
the static problem to a framework allowing for cavitation.
The talk is partly based on joint work with Manuel Friedrich (FAU Erlangen-Nuernberg)
and Carlos Mora-Corral (Universidad Autonoma de Madrid).

Jaroslav Kruis (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University)
2023-11-20 14:40 - 16:10
Title: Hydro-thermo-mechanical simulation of deep geological repository of radioactive waste (https://master.researchseminars.org/talk/NSCM/125/)
by Jaroslav Kruis (Department of Mechanics, Faculty of Civil Engineering, Czech Technical University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Possible variants of deep geological repository will be introduced. Selected
engineering problems connected with the deep repositories will be summarized
and the appropriate mathematical models and numerical methods for their
solution will be described. The first problem is heat transfer caused by the
radioactive waste in steel-based containers of length about 5 meters. The
sizes of studied domain are approximately one kilometer and the investigated
period is thousands of years long. A combination of suitable numerical
methods has to be used in order to finish the numerical simulations in
reasonable time. The second problem is thermo-hydro-mechanical (THM)
analysis of a system container-bentonite layer-surrounding rock massif. It
is based on the balance equation of momentum, mass and energy together with
various constitutive relationships. The THM analysis is formulated for 2D
and 3D.

New Year
2024-01-01 14:40 - 16:10
by New Year as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Leon Happ (TU Wien)
2024-03-11 14:40 - 16:10
Title: Extension operators for homogenization that preserve target manifold constraints (https://master.researchseminars.org/talk/NSCM/128/)
by Leon Happ (TU Wien) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Motivated by homogenization problems in micro-magnetics and plasticity, we study the existence of extension operators for W^{1,p} Sobolev maps on periodically perforated domains, where the maps are only allowed to range in some prescribed Riemannian manifold. For applications, one demands that separate L^p bounds for the extension and its gradient, independent of the scale of the perforations, hold. We stress that the main novelty of our work lies in the fact that all functions are subject to a manifold constrained in the target space. The challenge is then to find an extension operator preserving this feature. It turns out that this is a problem sitting right at the interface between analysis and algebraic topology.

The unconstrained case was famously treated in an influential paper by E. Acerbi, V. C. Piat, G. Dal Maso, and D. Percivale from 1992, providing a positive answer for all p except infinity. However, as soon as one starts to include manifold constraints, the existence problem of extensions becomes highly sensitive towards the relation between p and d and calls for a case differentiation. It can be shown that, due to Sobolev embeddings, for p bigger or equal than d the question whether every Sobolev function on a perforated domain possesses an extension reduces to a similar question for continuous functions. This is a problem well studied in algebraic topology and, in theory, there are tools available to determine its answer.

These observations lead us to focus on the case that p is smaller than d (e.g., in the physically relevant instance that p=2, d=3). Then, for p>1, we can indeed proof the existence of an extension operator as described above, and under the additional assumption that the target manifold is [p-1] connected (where [] is the floor function), meaning that the first [p-1] fundamental groups of N are trivial. The proof builds upon the already alluded result by E. Acerbi, V. C. Piat, G. Dal Maso, and D. Percivale, combining it with an appropriate retraction onto the target manifold, firstly suggested by R. Hardt and F.-H. Lin in 1987, and originating again from algebraic topology. It is important to note that the extension operator will not be linear. Already the target manifold constraint is not compatible with linearity.

In my talk, I will put a special emphasis on illuminating the [p-1]-connectedness condition that arises from the construction of the retraction onto N. The same assumption is already well-known in the context of the Sobolev functions between manifolds, where, for instance, it determines the surjectivity of the trace operator. This is only one example of a deeper connection that I will unveil.

Marco Morandotti (Politecnico di Torino)
2024-02-19 14:40 - 16:10
Title: From game theory to the control of multi-agent systems (https://master.researchseminars.org/talk/NSCM/129/)
by Marco Morandotti (Politecnico di Torino) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Motivated by the analysis of evolutive systems of agents with strategies, we enrich the structure of the celebrated replicator equation to include more realistic scenarios suitable for game-theoretic applications. In this context, non-linear continuity equations arise to describe the evolution of the mean-field limit of such systems. Starting from simple cases, we discuss more sophisticated models, which include the interplay between the evolution of the position of the players and the evolution of their strategies; the addition of a control factor that models the presence of a policy maker in multi-population dynamics, together with the rise and fall of leadership; the effects of an entropic regularisation in the system, as well as that of fluctuations.

We present the derivation of these equations, together with some well-posedness results.

Bernd Schmidt (University of Augsburg)
2024-02-26 14:40 - 16:10
Title: On the Stability of Objective Structures (https://master.researchseminars.org/talk/NSCM/130/)
by Bernd Schmidt (University of Augsburg) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We discuss the stability of objective structures of interacting atoms that form a far reaching generalization of crystal lattices. To this end, we use methods from harmonic analysis to set up a second derivative test of the configurational energy at equilibria, a key point being the identification of a carefully chosen seminorm with respect to which coercivity is estimated. In particular, a novel discrete Korn type inequality is established in the setting of objective structures. We also provide an efficient algorithm to check for atomistic stability which we illustrate numerically for a general carbon nanotube. (This is joint work with M. Steinbach, Augsburg)

Marco Bresciani (University of Erlangen)
2024-04-15 13:40 - 15:10
Title: Variational models with Eulerian-Lagrangian formulation allowing for material failure (https://master.researchseminars.org/talk/NSCM/131/)
by Marco Bresciani (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We investigate the existence of minimizers of variational models with Eulerian-Lagrangian
formulations. Similar models arise naturally in many multi-physics problems such as
the modeling of nematic and ferromagnetic elastomers. We consider energy functionals
depending on the deformation of a body, defined on its reference configuration, and an
Eulerian map defined on the unknown deformed configuration in the actual space. Our
existence theory moves beyond the purely elastic setting and accounts for material failure
by addressing free-discontinuity problems where both deformations and Eulerian fields are
allowed to jump. To do so, we build upon the work of Henao and Mora-Corral regarding
the variational modeling of cavitation and fracture in nonlinear elasticity. Two main
settings are considered by modeling deformations as Sobolev and SBV -maps, respectively.
The regularity of Eulerian maps is specified in each of these two settings according to the
geometric and topological properties of the deformed configuration. Effectiveness and
limitations of the theory are illustrated by means of explicit examples.
The talk is based on joint work with Manuel Friedrich (FAU Erlangen-Nuremberg) and
Carlos Mora-Corral (Universidad Autonoma de Madrid).

Giovanni Fantuzzi (University of Erlangen)
2024-05-13 13:40 - 15:10
Title: Moment-Sum-of-Squares relaxations for variational problems (https://master.researchseminars.org/talk/NSCM/132/)
by Giovanni Fantuzzi (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Moment-Sum-of-Squares (moment-SOS) relaxations are an established technique to compute converging sequences of lower bounds on the global minimum of finite-dimensional polynomial optimization problems. In this talk, I will discuss two recent extensions of moment-SOS relaxations to infinite-dimensional variational problems, where a (possibly nonconvex) integral functional is to be minimized over functions from a Sobolev space. The first extension optimizes so-called "null Lagrangian translations" and returns certified lower bounds on the global minimum of the variational problem. The second extension, instead, produces upper bounds by approximating minimizers of finite element discretizations of the variational problem. Conditions that ensure the convergence of these upper and lower bounds to the desired global minimum will be discussed, and current gaps between theory and practice will be illustrated by means of examples.

Hywel Normington (University of Strathclyde)
2024-04-22 13:40 - 15:10
Title: A decoupled, convergent and fully linear algorithm for the Landau-Lifshitz-Gilbert equation with magnetoelastic effects (https://master.researchseminars.org/talk/NSCM/133/)
by Hywel Normington (University of Strathclyde) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The mechanical and magnetic properties of ferromagnetic materials are strongly coupled. Applying a stress to a ferromagnetic material changes the magnetic state, and applying a magnetic field deforms it. These fall collectively under the phenomena of "magnetostriction". We consider the coupled system of the Landau-Lifshitz-Gilbert (LLG) equation and conservation of momentum to describe magnetostrictive processes. For this nonlinear system of time-dependent partial differential equations, we present a decoupled and unconditionally convergent integrator based on linear finite elements in space and a one-step method in time. Compared to previous works on this problem, for our method, we prove a discrete energy law that mimics that of the continuous problem. Moreover, we do not employ a nodal projection to impose the unit-length constraint on the discrete magnetization, so that the stability of the method does not require weakly acute meshes. Furthermore, our integrator and its analysis hold for a more general setting, including body forces and traction, and a more general representation of the magnetostrain.

H. Normington and M. Ruggeri, A decoupled, convergent and fully linear algorithm for the Landau--Lifshitz--Gilbert equation with magnetoelastic effects.
(under review),
https://arxiv.org/abs/2309.00605v2

break
2024-01-29 14:40 - 16:10, 2024-02-05 14:40 - 16:10, 2024-02-12 14:40 - 16:10
by break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Jan Scherz (University of Wuerzburg)
2024-04-08 13:40 - 15:10
Title: Weak Solutions to Mathematical Models of the Interaction between Fluids, Solids and Electromagnetic Fields (https://master.researchseminars.org/talk/NSCM/137/)
by Jan Scherz (University of Wuerzburg) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We prove the existence of weak solutions to two systems of PDEs modeling interactions between fluids, solids and electromagnetic fields. The first problem we consider describes the motion of an insulating rigid body through an electrically conducting incompressible fluid. The existence of weak solutions to this problem is achieved via a time discretization and an application of the Brinkman penalization. The second considered problem deals with the evolution of the deformation and the magnetization of a magnetoelastic material and is solved via an application of De Giorgi's minimizing movements scheme.

Easter Monday
2024-04-01 13:40 - 15:10
Title: no talk (https://master.researchseminars.org/talk/NSCM/138/)
by Easter Monday as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Eduard Rohan (University of West Bohemia, Pilsen)
2024-03-25 14:40 - 16:10
Title: Homogenization based model of flows in piezoelectric porous metamaterials driven by peristaltic deformation (https://master.researchseminars.org/talk/NSCM/139/)
by Eduard Rohan (University of West Bohemia, Pilsen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The seminar talk is devoted to the multiscale modelling of an electroactive porous material intended for fluid transport. Its functionality is based on the peristaltic flow which is induced by deforming pore walls. This phenomenon is of a great importance in physiology and biomechanics, however, as a driving mechanism of fluid transport, it presents and important and challenging issue in the design of smart ``bio-inspired'' materials. We consider locally periodic porous structures saturated by a Newtonian fluid. The peristaltic deformation wave of the microchannels is induced by a convenient local control of piezoelectric segments. Several issues related to the construction of a computationally efficient two-scale metamaterial model within the homogenization framework will be presented. We consider relatively small deformation which enables to use the linear kinematic framework. The poro-piezoelectric model derived in [1] is extended for the viscous fluid flow while respecting the inertia effects in both the phases. Using the homogenization based on the classic asymptotic analysis, cell problems (at the microlevel) are obtained which provide characteristic responses of the microstructures with respect to macroscopic strains, fluid pressure and electric potentials. These responses are needed to compute the effective (homogenized) parameters of the macroscopic problem which depend on the microconfiguration. The numerical studies demonstrate that such a linear model cannot capture the desired pumping effect of the homogenized continuum. To achieve this functionality of the model, it is necessary to account for the nonlinearity associated with deformation-dependent microconfigurations. To avoid hurdles associated with a fully nonlinear two-scale model, we apply a linearization procedure based on the sensitivity analysis of the local characteristic responses with respect to the deformation induced by the macroscopic quantities. In this way, by virtue of the methodology introduced in [2], we get first-order expansions of all the homogenized coefficients. The dynamic effects lead to the macroscopic flow model in a convolution form. For this option, a special treatment of the deformation-dependent dynamic permeability is needed. Numerical examples illustrate efficiency of the proposed computational approach [3].

[1] E. Rohan, V. Lukeš. On modelling nonlinear phenomena in deforming heterogeneous media using homogenization and sensitivity analysis concepts. Applied Mathematics and Computation (2015) 267:583-595.

[2] E. Rohan, V. Lukeš. Homogenization of the fluid-saturated piezoelectric porous media. Int. Jour. Solids and Structures (2018) 147:110-125.

[3] E. Rohan, V. Lukeš. Homogenization of peristaltic flows in piezoelectric porous media. (2023) arXiv:2304.05393v1, https://doi.org/10.48550/arXiv.2304.05393

Chiara Gavioli (Czech Technical University, Prague)
2024-04-29 13:40 - 15:10
Title: A model for lime consolidation of porous solids (https://master.researchseminars.org/talk/NSCM/140/)
by Chiara Gavioli (Czech Technical University, Prague) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We present the first mathematical 3D model describing the process of filling the pores of a building material with a water-lime-mixture, with the goal to improve the consistency of the porous solid. Chemical reactions produce calcium carbonate which glues the solid particles together at some distance from the boundary and strengthens the whole structure. The model consists of a reaction-diffusion system with a nonlinear non-smooth boundary condition, coupled with the mass balance equations for the chemical reaction. The main result consists in proving that the system has a solution for each initial data from a physically relevant class. A 1D numerical test shows a qualitative agreement with experimental observations.
This is a joint work with B. Detmann (Universität Duisburg-Essen), P. Krejčí, J. Lamač, and Y. Namlyeyeva (Czech Technical University Prague).

Johannes Zimmer (Technical University of Munich)
2024-05-06 13:40 - 15:10
Title: Deriving a GENERIC system from a Hamiltonian system (https://master.researchseminars.org/talk/NSCM/141/)
by Johannes Zimmer (Technical University of Munich) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We reconsider the problem of coarse-graining infinite-dimensional Hamiltonian dynamics to obtain a macroscopic system that includes dissipative mechanisms. In particular, we study the thermodynamical implications concerning Hamiltonians, energy, and entropy and the induced geometric structures. The Hamiltonian model is described by a unitary group, and is time-reversible. The coarse-grained description includes dissipative effects, is described by a contraction semigroup, and is thus irreversible. The concepts of dilations and contractions will be described as they provide a link between dissipative semigroups and unitary groups. The coarse-grained version will be shown to have GENERIC (General Equations for Non-Equilibrium Reversible Irreversibe Coupling) structure, with conserved energy, nondecreasing entropy and an Onsager operator describing the dissipation.

This is joint work with Alex Mielke and Mark Peletier.

Giuseppe Tomassetti (University of Roma Tre)
2024-03-18 14:40 - 16:10
Title: A mechanical model of ocular bulb vibrations and implications for acoustic tonometry (https://master.researchseminars.org/talk/NSCM/142/)
by Giuseppe Tomassetti (University of Roma Tre) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We propose a comprehensive mechanical model of ocular bulb vibrations and discuss its implications for acoustic tonometry. The model describes the eye wall as a spherical, pre-stressed elastic shell containing a viscoelastic material and accounts for the interaction between the elastic corneoscleral shell and the viscoelastic vitreous humor. We investigate the natural frequencies of the system and the corresponding vibration modes, expanding the solution in terms of scalar and vector spherical harmonics. From a quantitative point of view, our findings reveal that the eyebulb vibration frequencies significantly depend on IOP. This dependency has two origins: "geometric" stiffening, due to an increase of the pre-stress, and "material" stiffening, due to the nonlinearity of the stress-strain curve of the sclera. The model shows that the second effect is by far dominant. We also find that the oscillation frequencies depend on ocular rigidity, but this dependency is important only at relatively large values of IOP. Thus close to physiological conditions, IOP is the main determinant of ocular vibration frequencies. The vitreous rheological properties are found to mostly influence vibration damping. This study contributes to the understanding of the mechanical behavior of the eye under dynamic conditions and thus has implications for non-contact intraocular pressure measurement techniques, such as acoustic tonometry. The model can also be relevant for other ocular pathological conditions, such as traumatic retinal detachment, which are believed to be influenced by the dynamic behavior of the eye.

Václav Mácha (Institute of Mathematics, Czech Academy of Sciences)
2024-03-04 14:40 - 16:10
Title: ANALYSIS OF A SYSTEM MODELLING THE INTERACTION BETWEEN THE MOTION OF PISTON-SPRING AND A VISCOUS GAS (https://master.researchseminars.org/talk/NSCM/143/)
by Václav Mácha (Institute of Mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We are concerned with a one-dimensional flow of a compressible
fluid which may be seen
as a simplification of the flow of fluid in a long, thin pipe. We assume
the pipe is on one side,
ending by a spring. The other side of the pipe is left open – there, we
assume either inflow or outflow
boundary conditions. Such a situation can be understood as a toy model for
human lungs. We tackle
the question of uniqueness and the existence of a strong solution for a
system modeling the above process,
special emphasis is laid upon the estimate of the maximal time of
existence.
This is a joint work with Sabrine Chebbi and Šárka Nečasová

Pavel Krejčí (Czech Technical University in Prague, Faculty of Civil Engineering)
2024-05-20 13:40 - 15:10
Title: Hysteresis in porous media (https://master.researchseminars.org/talk/NSCM/144/)
by Pavel Krejčí (Czech Technical University in Prague, Faculty of Civil Engineering) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We propose a model for fluid diffusion in partially saturated porous media taking
into account saturation-dependent permeability as well as hysteresis effects in the pressure saturation relation. The resulting mathematical problem leads to a diffusion equation for
the pressure in an N-dimensional domain with a Preisach hysteresis operator under the time
derivative and in the diffusion coefficient. The problem is doubly degenerate in the sense
that the saturation range is bounded, and no a priori control of the time derivative of the
pressure is available. We discuss the conditions for existence and uniqueness of a solution
to the problem with or without gravity effects in appropriate function spaces, as well as the
question of bounded speed of propagation. This is a joint work with Chiara Gavioli.

summer break
2024-05-27 13:40 - 15:10
Title: We'll continue on September 30, 2024 (https://master.researchseminars.org/talk/NSCM/145/)
by summer break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Matteo Negri (University of Pavia)
2024-10-21 13:40 - 15:10
Title: Rate-independent evolutions in phase-field fracture generated by equilibrium configurations (https://master.researchseminars.org/talk/NSCM/146/)
by Matteo Negri (University of Pavia) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In the phase-field approach, and in other regularized fracture models, rate-independent (quasi-static) evolutions are usually obtained by means of time-discrete schemes, providing at each time an equilibrium configuration of the system. Numerically, equilibria are computed by descent methods for the free energy (e.g. staggered, monolithic etc.) endowed with a suitable irreversibility constraint on phase-field parameter (e.g. monotonicity in time). The time-continuous limit evolution is characterized in terms of evolutionary variational inequalities and in terms of Griffith's criterion. The study of the limit evolution reveals a couple of propagation regimes: stable (or steady state) and unstable (or catastrophic). In the stable regime the evolution is simultaneous (in displacement and phase field parameter) and satisfies Griffith's criterion in terms of toughness and phase field energy release rate. In the unstable regime the evolution is not necessarily simultaneous and may not satisfy Griffith's criterion. Energy identity holds in general with an instantaneous drop of energy in unstable times. The monotonicity constraint turns out to be fully thermodynamically consistent along the whole evolution. Technically, the proof relies on: (a) the strong convergence of the phase field parameter, (b) Kuratowski convergence of parametrized discrete times, (c) the limit of the power identity. The result is very general since it works independently of the scheme employed in the incremental problem, it holds for instance for AT1 and AT2 energies, in plane strain and plane stress settings. Numerically, we compare energies, energy release rates and evolutions computed in the sharp crack and in the phase field setting for a couple of reference benchmarks: the double cantilever beam (for steady state propagation) and the single edge notch under tension (for unstable propagation).

Vladislav Mantič (University of Sevilla)
2024-09-30 13:40 - 15:10
Title: Stress singularities in BVPs with Robin and Ventcel boundary conditions. Applications in FEM modeling (https://master.researchseminars.org/talk/NSCM/147/)
by Vladislav Mantič (University of Sevilla) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Linear-elastic antiplane-strain problems governed by the 2D Laplace equation are considered in domains with corners and cracks. First, power-logarithmic stress singularities in Neumann-Robin BVPs in infinite corner (polar sector) type domains are studied. Asymptotic solutions given by a double asymptotic series with the main and the associated shadow terms are presented. An application of such an asymptotic series to the numerical solution of the BVP of a crack in a thin adhesive interface layer modeled by the spring interface is shown by implementing a finite element method (FEM) procedure. Second, similar asymptotic analysis of power-logarithmic stress singularities in Dirichlet-Robin BVPs in infinite corners with a power-law variation (with the distance to the corner apex) of the governing coefficient in the Robin boundary condition is presented. An application of such an asymptotic solution to the BVPs of bridged cracks with a power-law variation of the stiffness of linear-elastic spring distribution is presented. Finally, a power-logarithmic stress singularity in a Dirichlet-Ventcel BVP in half domain is studied by a similar asymptotic procedure. An application of this asymptotic solution to the FEM solution of a BVP with a finite and open Gurtin-Murdoch material surface is presented.

Pablo Pedregal (University of Castilla-La Mancha)
2024-11-18 14:40 - 16:10
Title: Discoveries and surprises in the non-local Calculus of Variations (https://master.researchseminars.org/talk/NSCM/148/)
by Pablo Pedregal (University of Castilla-La Mancha) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Peridynamics stands as a main application of non-local variational problems in Continuum Mechanics. Yet from the mathematical point of view many of the important issues behind are formally similar, after suitable non-local reinterpretation of tools, to the classic local framework. Though this is no doubt surprising and reassuring, we will try to push non-locality to find some situations where things are really different. Some of the simplest examples will serve to illustrate how different things may be.

Cristiana De Filippis (University of Parma, Italy)
2024-11-25 14:40 - 16:10
Title: Regularity problems in the Calculus of Variations (https://master.researchseminars.org/talk/NSCM/149/)
by Cristiana De Filippis (University of Parma, Italy) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Regularity theory and the Calculus of Variations are unavoidably linked to each other,
as in fact, regularity techniques essentially serve to show weak or distributional solutions are in
fact classical solutions. Therefore, regularity ensures solvability. This is a topic that has been tremendously developed over the last 100 years, and I will try to give an overview starting from very
classical results, passing through the fundamental contributions of De Giorig and Nash, eventually
approaching some of the most recent developments involving nonuniformly elliptic problems.

////////////////
2024-10-28 14:40 - 16:10
Title: National Holiday - no seminar lecture (https://master.researchseminars.org/talk/NSCM/150/)
by //////////////// as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

X-mas
2024-12-23 14:40 - 16:10, 2024-12-16 14:40 - 16:10, 2024-12-30 14:40 - 16:10
by X-mas as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Anna Hundertmark (Rheinland-Pfälzische Technische Universität)
2024-10-07 13:40 - 15:10
Title: Modeling of carotid artery hemodynamics towards a CFD database for stroke risk assessment (https://master.researchseminars.org/talk/NSCM/152/)
by Anna Hundertmark (Rheinland-Pfälzische Technische Universität) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In medicine, the risk assessment of strokes caused by pathological
irregularities in the bifurcation of the carotid artery plays a major
role in the patient's optimal treatment decision.
This decision-making process can be greatly enhanced by detailed flow
field data obtained from simulations using patient-specific arterial
morphologies. We present our numerical modeling approach to create a CFD
database that can guide stroke risk assessment, including hemodynamic shear risk
metrics. We investigate the multi-directional behavior of wall shear
stress (WSS) based on specially
constructed longitudinal tangent vectors using a center-line projection
approach and present the utility of longitudinal WSS evaluation for
detecting opposing or transverse WSS in slow patient-specific flow. In
our fluid-structure interaction model,
we generalize the assumption of linear elasticity by a strain-dependent
elastic modulus that is consistent with laboratory measurements of
compliance and distensibility. Finally, we present the established
working pipeline to generate CFD
data for a large number of patient-specific geometries. Created
hemodynamic datasets can be used for visual atlases and comparative
analysis or explored by neural networks.

Matteo Caggio (Institute of mathematics, Czech Academy of Sciences)
2024-10-14 13:40 - 15:10
Title: Vanishing viscosity limit for the compressible Navier-Stokes equations with non-linear density dependent viscosities (https://master.researchseminars.org/talk/NSCM/153/)
by Matteo Caggio (Institute of mathematics, Czech Academy of Sciences) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In a three-dimensional bounded domain, we consider the compressible
Navier-Stokes equations for a barotropic fluid with general non-linear
density dependent viscosities and no- slip boundary conditions. A
nonlinear drag term is added to the momentum equation. We establish two
conditional Kato-type criteria for the convergence of the weak solutions
to such a system towards the strong solution of the compressible Euler
system when the viscosity coefficient and the drag term parameter tend
to zero.

Angela Bašič-Šiško (University of Rijeka)
2024-11-04 14:40 - 16:10
Title: Real micropolar gas flow model (https://master.researchseminars.org/talk/NSCM/154/)
by Angela Bašič-Šiško (University of Rijeka) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The micropolar real gas model, which extends the traditional fluid
dynamics model to account for micro-effects, is explored. This model
introduces additional rotational degrees of freedom to capture the
behavior of the internal fluid structure. By incorporating the
equation
of state for real gases, a shift from the ideal gas model to a more
general case is achieved. The mathematical framework of this model is
discussed, and results on the existence, uniqueness, and large-time
behavior of the solution for one-dimensional and spherically symmetric
flows are presented.
Furthermore, we consider combustion within the fluid to form the
reactive micropolar real gas model. This model additionally
incorporates
the chemical reactivity of the gas mixture, enabling the simulation of
reactive flows such as fuel combustion, detonation in aerospace
engineering, and the modeling of gaseous stars. Results on the
well-posedness of this model are also presented.

Riccardo Voso (University of Vienna)
2024-11-11 14:40 - 16:10
Title: Weighted Energy-Dissipation approach to gradient flows (https://master.researchseminars.org/talk/NSCM/157/)
by Riccardo Voso (University of Vienna) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The Weighted Energy-Dissipation variational approach has been extensively applied to gradient flows in the last decade. A family of parameter-dependent functionals defined over entire trajectories is introduced and proved to admit global minimizers. These global minimizers correspond to solutions of elliptic-in-time regularizations of the limiting causal problem. By passing to the limit in the parameter, such global minimizers converge, up to subsequences, to a solution of the gradient flow. After discussing such variational formulation in the context of classical gradient flows, we will focus on the semilinear gradient flows with state-dependent dissipation.
This is partly based on a joint work with Goro Akagi and Ulisse Stefanelli.

Gabriele Sbaiz (University of Trieste)
2024-12-09 14:40 - 16:10
Title: Fast rotation and inviscid limits for the SQG equation with general ill-prepared initial data (https://master.researchseminars.org/talk/NSCM/158/)
by Gabriele Sbaiz (University of Trieste) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In the talk, we study the fast rotation and inviscid limits for the 2-D dissipative surface quasi-
geostrophic equation with a dispersive forcing term, in the domain Ω = T1 × R. In the case
when we perform the fast rotation limit (keeping the viscosity fixed), in the context of general
ill-prepared initial data, we prove that the limit dynamics is described by a linear equation with
parabolic structure. Conversely, performing the combined fast rotation and inviscid limits, we
show that the means of the target initial datum ϑ0 are conserved along the motion. The proof
of the convergence is based on a compensated compactness argument which allows, on the one
hand, to get compactness properties for suitable quantities hidden in the wave system and, on
the other hand, to exclude the oscillatory part of waves at the limit.

Pavel Krejčí (Faculty of Civil Engineering, CTU & Institute of Mathematics, CAS)
2024-12-02 14:40 - 16:10
Title: Non-convex variational inequalities in contact mechanics (https://master.researchseminars.org/talk/NSCM/159/)
by Pavel Krejčí (Faculty of Civil Engineering, CTU & Institute of Mathematics, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We propose a new mathematical model for the dynamics of a rail
represented by a straight elastic or elastoplastic beam in contact with
the foundation and subject to a moving load. The foundation consists of
a granular material which undergoes irreversible structural changes such
as grain degradation and decreasing void ratio. The theory of non-convex
sweeping processes makes it possible to evaluate the energy exchange
between the rail and the foundation, and to exploit the energy balance
equation to prove existence and uniqueness of solutions to the full
system consisting of a fourth order PDE coupled with a variational
inequality with a non-convex state-dependent constraint.

Winter Break
2025-01-06 14:40 - 16:10, 2025-01-13 14:40 - 16:10, 2025-01-20 14:40 - 16:10, 2025-01-27 14:40 - 16:10, 2025-02-03 14:40 - 16:10, 2025-02-10 14:40 - 16:10
by Winter Break as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Jan Kristensen (University of Oxford)
2025-03-03 14:40 - 16:10
Title: Existence results in elasticity beyond polyconvexity (https://master.researchseminars.org/talk/NSCM/166/)
by Jan Kristensen (University of Oxford) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In this talk I discuss some recent results in the calculus of variations that yield existence of minimizers in spaces of Sobolev homeomorphisms for a natural class of elastic energies.
The presented results are part of a joint work with Kari Astala, Daniel Faraco, Andre Guerra
and Aleksis Koski.

Kai Richter (Institute of Scientific Computing, TU Dresden)
2025-03-10 14:40 - 16:10
Title: Dimension reduction for elastoplastic rods in the bending regime (https://master.researchseminars.org/talk/NSCM/167/)
by Kai Richter (Institute of Scientific Computing, TU Dresden) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In our work we rigorously derive a limiting bending model for thin rods, starting from a full 3D model for finite elastoplasticity. For the derivation we lean on the framework of evolutionary Gamma-convergence for rate-independent systems, introduced by Mielke, Roubíček and Stefanelli in 2008. The main difficulty here is to establish a mutual recovery sequence for the stored energy and dissipation. Strategies have been developed by various authors in order to construct such a sequence, e.g. for linearization or in the von Kármán regime. However, these rely on considering infinitesimal deformations in the limit, which we cannot expect in the bending regime. Our approach relies on a construction based on a multiplicative decomposition of the rotation fields obtained via the rigidity estimate from Friesecke, James and Müller. In order to achieve enough regularity, we consider strain gradient terms in the energy, which act on the two parts of the polar decomposition individually. These terms vanish in the limit.
This is joined work with Stefan Neukamm.

Marco Morandotti (Politecnico di Torino)
2025-03-24 14:40 - 16:10
Title: Replicator dynamics as the large population limit of a discrete Moran process (https://master.researchseminars.org/talk/NSCM/168/)
by Marco Morandotti (Politecnico di Torino) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The replicator dynamics accomplishes the task of modelling the evolution of strategies in a population by subjecting the probability of reproduction to their fitness: The higher the fitness, the higher the chance of being selected to reproduce. Yet, the criterion followed by individual agents to select their strategies is latent in the replicator equation, which describes the continuous-time evolution of the proportions of strategies in an averaged fashion.

In this talk, we provide a mathematical framework to derive the replicator equation as a mean-field limit of a discrete stochastic process modelling this evolutionary mechanism from the point of view of individual agents and their pairwise interactions. In this context, the classical Moran process is a prototypical example of discrete stochastic process that models natural selection in finite populations with two strategies (alleles, in biology) competing for dominance. We study the mean-field limit of a generalised Moran process as the number of agents diverges and we show that, in the weak selection regime, it converges to the replicator dynamics.

Matteo Caggio (Mathematićal Institute, CAS)
2025-03-31 13:40 - 15:10
Title: Mach number regimes for capillary fluids (https://master.researchseminars.org/talk/NSCM/169/)
by Matteo Caggio (Mathematićal Institute, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The talk will be devoted to the high and low Mach number limit for
compressible capillary fluids with density dependent viscosity.
We will present recent results concerning weak-strong uniqueness
property and dispersion of the acoustic waves.

Andreas Vikelis (Faculty of Civil Engineering, CTU)
2025-02-17 14:40 - 16:10
Title: VARIATIONAL APPROACH FOR THERMODYNAMICS OUT OF EQUILIBRIUM (https://master.researchseminars.org/talk/NSCM/170/)
by Andreas Vikelis (Faculty of Civil Engineering, CTU) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The study of dynamic elasticity is a mainstay in Applied Mathematics and
Mechanics as it models materials able to accommodate large deformations
which are abundant in different physical and biological applications. While
there is a vast body of literature on the static case in vectorial elasticity, particularly within the fields of calculus of variations and elliptic partial differential equations, the dynamic case has traditionally received less attention.
In the first part of the talk, we present recent findings regarding the stability
and uniqueness properties of the evolution equations in (thermo)elasticity,
while in the second part we discuss the variational structure of such systems
and present schemes to construct consistent solutions, i.e. dissipating entropy and conserving energy.
Joint work with Myrto Galanopoulou, Konstantinos Koumatos and Athanasios Tzavaras.

Ondřej Kreml (Institute of Mathematics, CAS)
2025-02-24 14:40 - 16:10
Title: Time-periodic solutions to an interaction problem between compressible viscous fluids and viscoelastic beams (https://master.researchseminars.org/talk/NSCM/171/)
by Ondřej Kreml (Institute of Mathematics, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We study a nonlinear fluid-structure interaction problem
between a viscoelastic beam
and a compressible viscous fluid. The beam is immersed in the fluid
which fills a two-
dimensional rectangular domain with periodic boundary conditions in both
directions,
while both the beam and the fluid are under the effect of time-periodic
forces. By using
a decoupling approach, at least one time-periodic weak solution to this
problem is con-
structed which has a bounded energy and a fixed prescribed mass. The
lack of a priori
energy bounds is overcome by a series of estimates based on a careful
choice of parameters.
The time-periodic solution is constructed by a series of limit
procedures.
This is a joint work with V. Mácha, Š. Nečasová and S. Trifunović.

Jaroslav Hron (Mathematical Institute, Charles University)
2025-03-17 14:40 - 16:10
Title: Numerical investigation of blood flows with slip boundary conditions (https://master.researchseminars.org/talk/NSCM/172/)
by Jaroslav Hron (Mathematical Institute, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Most studies of patient-specific blood flow models prescribe a no-slip boundary condition at the walls. Although its implementation is straightforward, its validity at the blood-vessel wall interface is questionable. It has been suggested in (Nubar, 1971) for example, that a slip boundary condition can be considered for blood flow in certain situations. We will discuss some effects of prescribing the Navier-type slip boundary condition, which assumes a linear proportionality between the tangential part of the wall velocity and the shear stress using an additional parameter. Given some measured flow data, for example modern 4D-PC MRI image, we use variational data assimilation approach to estimate the Navier's slip parameter on the wall for real data.

Easter Monday
2025-04-21 13:40 - 15:10
Title: no seminar (https://master.researchseminars.org/talk/NSCM/173/)
by Easter Monday as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Noy Cohen (Technion, Haifa)
2025-04-08 13:40 - 15:10
Title: From micro to macro: Unraveling the origin of the counterintuitive response in spider silk fibers (https://master.researchseminars.org/talk/NSCM/174/)
by Noy Cohen (Technion, Haifa) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Faculty of Civil Engineering, CTU, Thákurova 7, Praha 6, Room B-168 EXCEPTIONALLY.

Abstract
Spider silk is an extraordinary protein material characterized by high strength and toughness. Upon exposure to high humidity, silk fibers experience a reduction in stiffness of several orders of magnitude, supercontraction (i.e., a shortening of up to ~60% in length), and twist. These counterintuitive responses originate from a unique polymeric structure made of crystalline domains that are embedded in a highly aligned amorphous matrix. Broadly, high humidity leads to water uptake by the silk, which in turn motivates the dissociation of intermolecular hydrogen cross-linking bonds.
In this talk, I will present energetically motivated models based on tools from statistical mechanics that shed light on the relations between the microstructure and the macroscopic behavior and capture the overall response of silk fibers. The models are validated through a comparison to experimental findings. The insights from these models provide a method to characterize the microstructural evolution of hydrogen-bond dominated networks and pave the way to the design of novel biomimetic fibers with non-trivial properties.

1) R. Olive and N. Cohen, “Deformation and failure mechanisms in spider silk fibers”, Journal of the Mechanics and Physics of Solids, 182:105480, 2024.

2) N. Cohen, “The underlying mechanisms behind the hydration-induced and mechanical response of spider silk”, Journal of the Mechanics and Physics of Solids, 172:105141, 2023.

3) N. Cohen and C.D. Eisenbach, “Humidity-Driven Supercontraction and Twist in Spider Silk”, Physical Review Letters, 128:098101, 2022.

4) N. Cohen, M. Levin, and C.D. Eisenbach, “On the origin of supercontraction in spider silk”, Biomacromolecules, 22:993-1000, 2021.

Please note the time and location change for this talk !!!

seminar meets on Tue
2025-04-07 13:40 - 15:10
Title: We meet onTuesday, April 8 (https://master.researchseminars.org/talk/NSCM/175/)
by seminar meets on Tue as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Marco Amato (Faculty of Civil Engineering, CTU)
2025-04-14 13:40 - 15:10
Title: Elastic solids under frictionless rigid contact and configurational force (https://master.researchseminars.org/talk/NSCM/176/)
by Marco Amato (Faculty of Civil Engineering, CTU) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
A homogeneous elastic solid, bounded by a flat surface in its unstressed configuration, undergoes a finite
strain when in frictionless contact against a rigid and rectilinear constraint, ending with a rounded or sharp
corner, in a two-dimensional formulation. With a strong analogy to fracture mechanics, it is shown that (i.) a
path-independent J–integral can be defined for frictionless contact problems, (ii.) which is equal to the energy
release rate G associated with an infinitesimal growth in the size of the frictionless constraint, and thus gives the
value of the configurational force component along the sliding direction. Furthermore, it is found that (iii.) such a configurational sliding force is the Newtonian force component exerted by the elastic solid on the constraint at the frictionless contact. Assuming the kinematics of an Euler-Bernoulli rod for an elastic body of rectangularshape, the results (i.)–(iii.) lead to a new interpretation from a nonlinear solid mechanics perspective of the
configurational forces recently disclosed for one-dimensional structures of variable length. Finally, approximate
but closed-form solutions (validated with finite element simulations) are exploited to provide further insight into
the effect of configurational forces. In particular, two applications are presented which show that a transverse
compression can lead to Eulerian buckling or to longitudinal dynamic motion, both realizing novel examples of
soft actuation mechanisms. As an application to biology, our results may provide a mechanical explanation for
the observed phenomenon of negative durotaxis, where cells migrate from stiffer to softer environments. Joint work with F. Dal Corso and D. Bigoni.

[1] Francesco Dal Corso, Marco Amato, and Davide Bigoni. “Elastic solids under frictionless rigid contact and
configurational force”. In: Journal of the Mechanics and Physics of Solids 188 (2024), p. 105673

Michael Dumbser (University of Trento)
2025-05-26 13:40 - 15:10
Title: On well-balanced finite difference, finite volume and discontinuous Galerkin schemes for the Einstein-Euler system of general relativity (https://master.researchseminars.org/talk/NSCM/177/)
by Michael Dumbser (University of Trento) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In this talk we present a new family of well-balanced conservative CWENO finite difference schemes and discontinuous Galerkin (DG) finite element schemes with subcell finite volume (FV) limiter for the numerical solution of the Einstein–Euler equations of general relativity based on a first order hyperbolic reformulation of the Z4 formalism. The first order Einstein-Euler Z4 system, which is composed of 64 equations, is analysed and proven to be strongly hyperbolic for a general metric. The well-balancing is achieved for arbitrary but a priori known equilibria by subtracting a discrete version of the equilibrium solution from the discretized time-dependent PDE system. Special care has also been taken in the design of the numerical viscosity so that the well-balancing property is achieved. As for the treatment of low density matter, e.g. when simulating massive compact objects like neutron stars surrounded by vacuum, we have introduced a new filter in the conversion from the conserved to the primitive variables, preventing superluminal velocities when the density drops below a certain threshold, and being potentially also very useful for the numerical investigation of highly rarefied relativistic astrophysical flows.

We furthermore present a novel family of central WENO finite difference schemes for a new first order reformulation of the classical BSSNOK system.

Thanks to these improvements, all standard tests of numerical relativity are successfully reproduced, reaching four main achievements: (i) we are able to obtain stable long term simulations of stationary black holes, including Kerr black holes with extreme spin, which after an initial perturbation return perfectly back to the equilibrium solution up to machine precision; (ii) a (standard) TOV star under perturbation is evolved in pure vacuum (ρ = p = 0) up to t = 1000 with no need to introduce any artificial atmosphere around the star; and, (iii) we solve the head on collision of two punctures black holes, that was previously considered untractable within the FO-Z4 formalism, (iv) we perform a stable long-time evolution of a rotating binary black hole merger based on the new CWENO schemes for first order reformulation of the BSSNOK system.

References

[1] M. Dumbser, O. Zanotti, E. Gaburro and I. Peshkov, A well-balanced discontinuous Galerkin method for the first–order Z4 formulation of the Einstein–Euler system, Journal of Computational Physics 504 (2024), 112875.

[2] M. Dumbser, O. Zanotti and I. Peshkov. High order discontinuous Galerkin schemes with subcell finite volume limiter and AMR for a monolithic first-order BSSNOK formulation of the Einstein-Euler equations, Physical Review D 110 (2024), 084015.

[3] M. Dumbser, O. Zanotti and G. Puppo, A monolithic first–order BSSNOK formulation of the Einstein–Euler equations and its solution with conservative finite difference CWENO schemes, Physical Review D, submitted.

Maria Neuss-Radu (University of Erlangen)
2025-04-28 13:40 - 15:10
Title: Effective interface laws for fluid flow and transport through reactive porous membranes (https://master.researchseminars.org/talk/NSCM/178/)
by Maria Neuss-Radu (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We consider a coupled model for fluid flow and transport in a domain consisting of two bulk regions separated by a thin porous layer. The thickness of the layer is of order $\varepsilon$ and the microscopic structure of the layer is periodic in the tangential direction also with period $\varepsilon$. The fluid flow is described by an instationary Stokes system, properly scaled in the fluid part of the thin layer. The evolution of the solute concentrations is described by a reaction-diffusion-advection equation in the fluid part of the domain and a diffusion equation (allowing different scaling in the diffusion coefficients) in the solid part of the layer. At the microscopic fluid-solid interface inside the layer nonlinear reactions take place. This system is rigorously homogenized in the limit $\varepsilon \to 0$, based on weak and strong (two-scale) compactness results for the solutions. These are based on new embedding inequalities for thin perforated layers including coupling to bulk domains. In the limit, effective interface laws for flow and transport are derived at the interface separating the two bulk regions. These interface laws enable effective mass transport through the membrane, which is also an important feature from an application point of view. This is a joint work with Markus Gahn (Universität Heidelberg).

Christoph Allolio (Mathematical Institute, Charles University)
2025-05-05 13:40 - 15:10
Title: Applied Continuum Modeling of (Sub)cellular Morphogenesis (https://master.researchseminars.org/talk/NSCM/179/)
by Christoph Allolio (Mathematical Institute, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Cellular phenomena at the microscopic level are usually modeled via molecular simulations. These simulations have the advantage of giving an accurate description of the molecular interactions that give rise to biological phenomena. However, they are computationally expensive and hard to interpret. In particular, they are not capable of giving a satisfactory view of slow processes, such as organelle morphogenesis or cell division. For this purpose, continuum models are preferable. These models can be validated by structural data (e.g. electron microscopy). However, they can also be directly parametrized by molecular simulations. I present such a "data-driven" model for large membrane deformations, e.g. induced by cell penetrating peptides as well as a more reductive morphoelastic model for bacterial division.

Karel Tůma (Mathematical Institute, Charles University)
2025-05-12 13:40 - 15:10
Title: Phase-field model for beta-to-omega transformation in titanium alloys (https://master.researchseminars.org/talk/NSCM/180/)
by Karel Tůma (Mathematical Institute, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In this talk, we revisit a phase separation model involving multiple wells, focusing on $\beta-\omega$ transformations observed in titanium alloys. We introduce a novel approach that alters the algebraic form of the interfacial free energy. This modification relaxes the conventional coercivity requirements on surface tensions within total-spreading scenarios and, crucially, eliminates the emergence of $\omega-\omega$ mixed phases—structures that are crystallographically forbidden. The capabilities of the new model are illustrated through basic numerical experiments, and we also describe the next steps toward more comprehensive, three-dimensional simulations of $\beta-\omega$ phase evolution in titanium systems.

summer break (We start again)
2025-06-02 13:40 - 15:10
Title: in the fall (https://master.researchseminars.org/talk/NSCM/181/)
by summer break (We start again) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Vladislav Mantič (University of Sevilla)
2025-10-06 13:40 - 15:10
Title: Asymptotic Solutions at the Tip of Interface Cracks and Multi-Material Corners with Frictional Contact in Linear Elastic Anisotropic Solids (https://master.researchseminars.org/talk/NSCM/182/)
by Vladislav Mantič (University of Sevilla) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
This study focuses on point singularities in the solutions of linear elastic BVPs for anisotropic solids in 2.5D (generalised plane strain). The stresses in these BVPs can be unbounded at singular points, also known as corners, where discontinuities exist in the solid geometry, material properties or boundary/interface conditions. The behaviour of elastic solutions at singular points is described by asymptotic expansions expressed as series of products of power-logarithmic terms in the radial coordinate and characteristic angular functions. The exponents of these terms are known as singularity exponents, while the coefficients of the series are referred to as generalised stress intensity factors (GSIFs).

This work aims to develop:

1) a specific semi-analytic procedure to determine the terms of these asymptotic series at the tip of interface cracks with frictional sliding contact between the crack faces; and

2) a general semi-analytic procedure to determine the terms of these asymptotic series at the tip of multi-material corners with frictional sliding contact at the outer faces and/or interfaces between the wedges, considering the Coulomb friction law.

These procedures are novel in that they lead to nonlinear eigenproblems for both the singularity exponents and the angles of frictional shear stresses in frictional contact zones. Both procedures are based on the Stroh formalism in complex variable for linear anisotropic elasticity.

The application of these procedures is demonstrated by some interesting examples. Finally, SingSol, an online app that implements the general semi-analytic procedure for singularity analysis of multimaterial corners, is briefly presented.

Michael Stingl (University of Erlangen)
2025-11-03 14:40 - 16:10
Title: On a new class of separable models in topology and material optimization (https://master.researchseminars.org/talk/NSCM/183/)
by Michael Stingl (University of Erlangen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Separable models are used in specialized optimization solvers
for structural optimization like the method of moving asymptotes (MMA)
for many years. In this presentation, we derive a so called exact
separable models using the Sherman-Morrison-Woodbury-Formula. In this
context, exact means that the model matches an approximated function
exactly, as long as the design of only one element is varied. In simple
cases, there is a 1-to-1 correspondence to the MMA model. In more
general situations, non-linear material parametrizations cause the exact
separable model to be non-convex, non-smooth or even discontinuous. To
cope with that, the sequential global programming (SGP) algorithm is used.
In the first part of the talk the concepts of exact separable models and
the SGP method are introduced and some theoretical results like a link
to the calculus of topological derivatives and convergence properties
are briefly discussed. In the second part, applications from various
areas of material and topology optimization are used to demonstrate the
accuracy and efficiency of the new approach.

Marco Bresciani (University of Erlangen and JKU Linz)
2025-11-10 14:40 - 16:10
Title: Quasistatic growth of cavities and cracks in the plane (https://master.researchseminars.org/talk/NSCM/184/)
by Marco Bresciani (University of Erlangen and JKU Linz) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We propose a model for the quasistatic growth of cavities and cracks in two-dimensional nonlinear elasticity. Cavities and cracks are modeled as discrete and compact subsets of a planar domain, respectively, and deformations are defined only outside of cracks. The model accounts for the irreversibility of both processes of cavitation and fracture, and it allows for the coalescence of cavities into cracks. Our main result shows the existence of quasistatic evolutions in the case of a finite number of cavities under an a priori bound on the number of connected crack components. This is joint work with Manuel Friedrich (JKU Linz).

State holiday
2025-11-17 14:40 - 16:10
Title: We do not meet this week (https://master.researchseminars.org/talk/NSCM/185/)
by State holiday as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Tomáš Kozubek (Technical University of Ostrava)
2025-10-13 13:40 - 15:10
Title: From Scalable AI to Hybrid Quantum: The IT4Innovations Computing Continuum (https://master.researchseminars.org/talk/NSCM/186/)
by Tomáš Kozubek (Technical University of Ostrava) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The presentation focuses on the AI- and QC-centred computing continuum at IT4Innovations (IT4I), showing how GPU-accelerated HPC, data services, and emerging quantum resources are being integrated to support modern AI workflows and near-term quantum experimentation. On the AI side, we outline platforms and tools that raise productivity for training and inference at scale (e.g., HyperQueue for heterogeneous scheduling, HEAppE and LEXIS for HPC-as-a-Service and federated workflows) and describe access routes that connect Czech users to EuroHPC capacity, including LUMI and forthcoming AI-Factory services. On the QC side, we detail the VLQ superconducting quantum computer (24 qubits, star-shaped topology) and its role in hybrid HPC–QC pipelines for optimisation, small-scale quantum chemistry, and quantum-enhanced ML, alongside practical enablers such as error-mitigation strategies and classical pre/post-processing on Karolina and partner EuroHPC systems. We position these capabilities within e-INFRA CZ and the EuroHPC ecosystem, highlight representative impacts across science, industry, and public administration (from crisis-management analytics to drug-discovery workflows), and sketch next steps: federating AI factories and quantum systems, operationalising VLQ within EuroHPC access schemes, and commissioning Barbora NG to expand AI-ready throughput. Together, these developments advance a usable path from today’s large-scale AI to tomorrow’s hybrid quantum-accelerated applications.

Filippo Riva (Faculty of Mathematics and Physics, Charles University)
2025-10-20 13:40 - 15:10
Title: A free boundary approach to quasistatic debonding (https://master.researchseminars.org/talk/NSCM/187/)
by Filippo Riva (Faculty of Mathematics and Physics, Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Debonding models describe the evolution of an adhesive membrane peeled away from a planar rigid substrate. When the process is sufficiently slow, inertial and viscous effects can be neglected, leading to a quasistatic setting. In this framework, debonding can be formulated as a variational evolution of sets. In the talk, I will present how to prove the existence of so-called energetic solutions for this formulation—based on global minimizers of a suitable functional together with an energy balance—by exploiting an equivalent rewriting of the model in terms of the celebrated one-phase Bernoulli free boundary problem. This is based on a joint work with E. Maggiorelli and E. Tolotti.
If time permits, I will also discuss the dynamic version of the problem, in which inertial effects are taken into account. In this setting, a wave equation on moving domains is coupled with a suitable criterion governing the evolution of such domains. The problem, formulated in collaboration with G. Lazzaroni, R. Molinarolo, and F. Solombrino, is still open.

Jan Valášek (Faculty of Mechanical Engineering, CTU)
2025-11-24 14:40 - 16:10
Title: Mathematical modelling of human phonation process (https://master.researchseminars.org/talk/NSCM/188/)
by Jan Valášek (Faculty of Mechanical Engineering, CTU) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In this talk the fluid-structure-acoustic interaction (FSAI) problem with a particular interest in application on the problem of human phonation is addressed. This problem consists of the three physical fields: a highly complex airflow, a vibrating elastic structure (vocal folds) and acoustics and their mutual interactions. The general mathematical model of FSAI problem will be described and the later simplifications of it will be discussed. Since the main sound source of the human phonation is generated by an unsteady flow in the complex configuration of vocal tract the aeroacoustics as a separate branch of acoustics will be introduced. The ultimate goal of the aeroacoustics is to establish a well solvable simplification of the full description provided by the Navier-Stokes equations (for compressible fluid). Due to recent advantages the computational aeroacoustics has attained also a high interest in the field of technical applications. In the end the numerical simulations of flow-induced vibrations of vocal folds and the propagation of sound through human vocal tract based on the previously mentioned approaches will be shown.

Miroslav Kolář (Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague)
2025-09-29 13:40 - 15:10
Title: Modeling of discrete dislocation dynamics by means of the mathematical theory of evolving curves (https://master.researchseminars.org/talk/NSCM/189/)
by Miroslav Kolář (Faculty of Nuclear Sciences and Physical Engineering Czech Technical University in Prague) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Dislocation dynamics (DD) has become a standard tool for analyzing
deformation microstructures. Fundamentals of dislocation theory have been
established in 1930s and later verified by first TEM experiments in 1950s.
The ultimate objective of DD is to fill the gap between fully continuous
models in the macroscopic scale based on crystal plasticity, and atomistic
models in nanoscale usually treated by the molecular dynamics methods.

In crystalline solids, dislocations represent irregularities or defects in
the crystal structure. Such defects are usually of the line character and
the characteristic unit of length of such defects is microns. These line
defects are the subject of both external forces applied on the crystal as
well as various internal mechanisms, and they evolve in the so-called slip
planes given by particular crystallographic orientation.

Our research interest is in the detailed and precise modeling of fundamental
mechanisms involving single or very few dislocations. Such a topic is
typically referred to as a discrete dislocation dynamics (DDD).

In our approach to DDD, a single dislocation carrying the plastic flow in
its respective slip plane is represented as an evolving planar curve. The
experimentally observed mechanism how dislocations evolve is of a
non-Newtonian type and can be schematically described as

normal velocity = curvature + external force,

where the curvature term approximates the self-stress of the dislocation
generated by a line tension. We treat this kind of evolution equation by the
direct (Lagrangian) approach resulting in the system of two degenerate
parabolic equations for parametrization of the single dislocation curve. We
solve this problem numerically by means of the flowing finite-volume method,
and we improve the stability of the numerical scheme by the suitable choice
of the external tangential velocity which helps to redistribute the
discretization points along the dislocation in an appropriate way.

We demonstrate our approach in several computational examples covering the
fundamental dislocation mechanisms and then we focus on the dislocation
cross-slip, which is considered as one of the key mechanisms of
microplasticity and still an open problem in general. We show how we modify
our method by the geodesic description of curves to treat the cross-slip
within our framework.

seminar cancelled
2025-10-27 14:40 - 16:10
Title: We do not meet this week. (https://master.researchseminars.org/talk/NSCM/190/)
by seminar cancelled as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Matteo Caggio (Institute of Mathematics, CAS)
2025-12-08 14:40 - 16:10
Title: Between low and strong stratification regimes for rotating heat-conducting fluids (https://master.researchseminars.org/talk/NSCM/191/)
by Matteo Caggio (Institute of Mathematics, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We consider the Navier-Stokes-Fourier system for a heat conducting
compressible fluid under the effects of rotation and stratification. We
investigate the low Mach, Rossby and Froude number limit towards a
quasi-geostrophic balance in a stratification range between the
so-called low and strong stratification regimes. The limit is studied in
the context of weak solutions with ill-prepared initial data. This is a
joint work with Gabriele Sbaiz (Trieste).

Ondřej Marek (Faculty of Nuclear Sciences, CTU)
2025-12-01 14:40 - 16:10
Title: Lattice Boltzmann method for compressible fluid flow and drag simulations (https://master.researchseminars.org/talk/NSCM/192/)
by Ondřej Marek (Faculty of Nuclear Sciences, CTU) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
This talk discusses the use of the lattice Boltzmann method (LBM) for
compressible fluid flow and its application in approximating drag and lift
coefficients of objects. A brief overview of fluid dynamics is followed by
an explanation of the LBM. Entropic LBM and multi-speed velocity models
used to simulate compressible fluid flow are described, along with a
generalization of their boundary conditions and a benchmark problem. Next,
an algorithm for numerically computing the drag and lift coefficients
specific for the LBM grid is derived for both incompressible and
compressible flows. Finally, a numerical study is performed for flow
around a cylinder and a NACA profile with the multi-speed ELBM model,
reference single-speed LBM models and the finite volume method compared
with results from published studies.

X-mas break (we do not meet)
2025-12-15 14:40 - 16:10, 2025-12-22 14:40 - 16:10, 2025-12-29 14:40 - 16:10
by X-mas break (we do not meet) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Anna Doležalová (Institute of Information Theory and Automation, CAS)
2026-01-05 14:40 - 16:10
Title: Mission p smaller than n-1: Possible - Nonlinear Elasticity Beyond Conventional Limits (https://master.researchseminars.org/talk/NSCM/196/)
by Anna Doležalová (Institute of Information Theory and Automation, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
In models of Nonlinear Elasticity, the natural physical deformation is a minimizer of an energy functional containing the integral of $|Df(x)|^p$, and we search for the minimizer in the Sobolev space $W^{1,p}(\Omega, R^n)$. In the previous results, one assumes that p is at least n-1 to ensure the non-interpenetration of matter.
In this talk we prove the lower semicontinuity of an energy functional that allows, for the first time, for $p$ less than $n-1$. Our class of admissible deformations consists of weak limits of Sobolev homeomorphisms. We also introduce a model that allows for cavitations by studying weak limits of homeomorphisms that can open cavities at some points. In that model we add the measure of the created surface to the energy functional and we again prove lower semicontinuity.
This is a joint work with Daniel Campbell and Stanislav Hencl.

Michele Zaccaron (UMA, ENSTA Paris)
2026-02-16 14:40 - 16:10
Title: Bending and twisting of electromagnetic waveguides (https://master.researchseminars.org/talk/NSCM/202/)
by Michele Zaccaron (UMA, ENSTA Paris) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Consider a reference homogeneous and isotropic electromagnetic waveguide
with a simply connected cross-section embedded in a perfect conductor. In
this setting, when the waveguide is straight, the spectrum of the associated
self-adjoint Maxwell operator with a constant twist (which may be zero) is
entirely essential, lies on the real line and is symmetric with respect to zero,
exhibiting a gap around the origin.
In this talk, we present new results on the effects of the geometric defor-
mations of bending and twisting on the spectrum of the Maxwell operator.
More precisely, we provide, on the one hand, sufficient conditions on the
asymptotic behaviour of the curvature and twist of a perturbed waveguide
ensuring the preservation of the essential spectrum. Our approach relies on
a Birman-Schwinger-type principle which has an interest of its own. On the
other hand, we give sufficient conditions, involving in particular the shape of
the cross-section, so that the geometrical deformation creates discrete spec-
trum within the gap, and give some insight into its localization. Finally, we
show some theoretical and numerical results further investigating the suffi-
cient condition involving the geometry of the cross-section.
Based on joint work with Philippe Briet, Maxence Cassier and Thomas Ourmieres-Bonafos.

P. Podio-Guidugli / L. Truskinovsky (Roma Tor Vergata / ESPCI Paris)
2026-04-13 14:00 - 16:00
Title: On internal distance interactions in continuum physics/Generalized Clapeyron's Theorem (https://master.researchseminars.org/talk/NSCM/204/)
by P. Podio-Guidugli / L. Truskinovsky (Roma Tor Vergata / ESPCI Paris) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Institute of Mathematics, CAS. Žitná 25, Praha 2, Blue Lecture Hall.

Abstract
P. Podio-Guidugli:
On internal distance interactions in continuum physics (online)

The typical distance interactions a continuum experiences are with agencies external to it. Today I shall offer a discussion of internal distance interactions, based on ongoing work with Eliot Fried. Firstly, I shall introduce the distance stress, a symmetric tensor which is a continuum-mechanics counterpart, similar to Cauchy stress, of the skew two-point force interactions usually considered in discrete mechanics. Secondly, I shall introduce the distance energy-flux, a vector field similar to heat flux whose divergence equals the net distance-mediated energy-exchange input at a point.

L. Truskinovsky: Generalized Clapeyron's Theorem

Clapeyron’s Theorem in classical linear elasticity provides a
way to explicitly express
the energy stored in an equilibrium configuration in terms of the work
of the forces applied
on the boundary. We derive several new integral relations which can be
viewed as nonlinear
analogs of this classical result, reinterpreting them as rather general
statements within Calculus of Variations. We also give dynamical
interpretation for the apparently lost work.

This seminar is dedicated to the memory of Dr. Miroslav Šilhavý.

Note the changes in the place, time, and the zoom link.

Jonathan Bevan (University of Surrey)
2026-04-20 13:40 - 15:10
Title: Two sharp Poincaré inequalities in $W^{1,\infty}(\Omega)$ for convex domains $\Omega \subset \mathbb{R}^d$. (https://master.researchseminars.org/talk/NSCM/205/)
by Jonathan Bevan (University of Surrey) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Two sharp Poincaré inequalities
$$ ||u-Lu||_{L^\infty(\Omega)} \leq C(\Omega)||\nabla u||_{L^{\infty}(\Omega)}$$
are proved for Lipschitz functions $u$ on convex domains $\Omega \subset \mathbb{R}^d$.
Here, $Lu$ is either the integral mean $\langle u \rangle$ of $u$ over $\Omega$ or its median value $\mathrm{med} \, u$.
The sharp constants in both cases can be interpreted geometrically, and the case that $Lu = \langle u \rangle$ we prove that
(i) among convex domains of equal measure balls have the best, i.e. the smallest, Poincar\'{e} constants, and
(ii) since $C(\Omega)$ is the maximum of a certain convex function $\zeta$, calculating $C(\Omega)$ for polygonal convex domains is a matter of ordering the valus $\zeta(V_i)$ where $V_1,\ldots,V_n$ are the vertices of $\Omega$. In this context, we introduce the idea of `magic points' and explore evidence for their existence in concrete cases. This talk is based on joint works with J. Deane and S. Zelik.

Lukáš Horný (Faculty of Mechanical Engineering, CTU Prague)
2026-04-27 13:40 - 15:10
Title: Mechanics of nonlinearly elastic tubes: Effect of axial prestretching and consequences for the biomechanics of human arteries (https://master.researchseminars.org/talk/NSCM/206/)
by Lukáš Horný (Faculty of Mechanical Engineering, CTU Prague) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Axial prestretching can significantly affect the mechanical response of an inflated tube. This phenomenon is known, for example in the biomechanics of the cardiovascular system, where arteries, if excised from a body, manifest non-negligible shortening. It is clear that longitudinal prestretching leads to a reduction in the axial deformation that accompanies the pressure pulse transmitted through a tube made of a material exhibiting large-strain stiffening. Somewhat surprisingly, however, longitudinal prestressing increases the arterial distensibility and thus contributes to a higher relative volume that can be transmitted during the pressure pulse. It even appears that some material models, such as the Gent strain energy density function, have an axial strain inversion point at which the axial strain remains constant during pressurization while the relative volume is at its maximum. However, due to age-related changes, the value of the arterial axial prestretch decreases significantly with age. Simulations considering nonlinear anisotropic material for the arterial wall show that even though this value decreases, it still has a beneficial effect on the value of circumferential distensibility. Similarly, during the transition from elastic to viscoelastic behavior, we observe that, from the perspective of the thin-walled tube inflation problem, the longitudinal prestretch is advantageous for the attainable volume.

Giacomo Vianello (Institute of Information Theory and Automation, CAS)
2026-02-23 14:40 - 16:10
Title: The behavior of an almost-minimizer of the relative perimeter near a boundary vertex of the container. (https://master.researchseminars.org/talk/NSCM/207/)
by Giacomo Vianello (Institute of Information Theory and Automation, CAS) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
It is known that the boundary of an almost-minimizer of the relative perimeter inside a smooth container satisfies Young's Law, namely, it meets the container boundary orthogonally. Much less is known when the container is nonsmooth. In this talk, I will describe some recent results concerning the behavior of an almost-minimizer of the relative perimeter near an isolated singularity (vertex) of its container boundary. I will show that, in dimension three, a phenomenon we call vertex-skipping occurs, that is, the boundary of an almost-minimizer cannot pass through a vertex of its container, while in higher dimensions the situation is more intricate, and a relation between the "aperture" of the vertex and the avoidance of the singularity emerges. I will conclude by discussing some related open questions. This is part of a joint project with Gian Paolo Leonardi (University of Trento).

Helmut Abels (University of Regensburg)
2026-05-18 13:40 - 15:10
Title: Uniform higher order estimates for the sharp interface limit of a Navier-Stokes/Allen-Cahn system (https://master.researchseminars.org/talk/NSCM/208/)
by Helmut Abels (University of Regensburg) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We consider the linearized system for the sharp interface limit of a Navier-Stokes/Allen-Cahn system around a suitable approximate solution.
With the aid of a suitable weight taking the distance to the interface and the interfacial thickness into account we obtain optimal regularity estimates, which are uniformly in the interfacial thickness. This enables to improve previous convergence results in two space dimensions significantly and extend results to three space dimensions. This is a joint-work with Mingwen Fei, Yadong Liu, and Maximilian Moser.

Giuseppe Tomassetti (University Roma Tre)
2026-03-09 14:40 - 16:10
Title: On the single field formulation in magnetostatics (https://master.researchseminars.org/talk/NSCM/210/)
by Giuseppe Tomassetti (University Roma Tre) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We systematically discuss the equivalence of two variational formulations of magnetostatics, in terms of the fields (H,M) on the one hand and the single field formulation using only B on the other hand. To demonstrate that this link is stable also when the magnetic laws are coupled with other variational static models, elasticity is included in the models as well. Interestingly, despite the fact that the corresponding magnetoelastic energy densities in the material can be computed via Legendre-Fenchel transform in the magnetic state variables, the two formulations are not linked by standard convex duality on the level of the functionals. In addition, convexity and coercivity of the given functional are neither required for the transformation nor always preserved by it.

Michele Ruggeri (University of Bologna)
2026-03-16 14:40 - 16:10
Title: Convergent finite element methods for nematic liquid crystals (https://master.researchseminars.org/talk/NSCM/211/)
by Michele Ruggeri (University of Bologna) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The Ericksen model describes nematic liquid crystals (LCs) in terms of a unit-length vector field (director) and a scalar function (degree of orientation). Compared to the classical Oseen-Frank model, it allows for the description of a larger class of defects. Equilibrium states of the LC are given by admissible pairs that minimize an energy functional, which consists of the sum of Oseen-Frank-like energies and a double well potential. The resulting Euler-Lagrange equations are degenerate for the director, which poses serious difficulties to formulate mathematically sound algorithms for their approximation. We propose a simple but novel finite element approximation of the problem that does not employ a projection to impose the unit-length constraint on the director and thus circumvents the use of weakly acute meshes,quite restrictive in 3D. We show stability and Gamma-convergence properties of the new method in the presence of defects. We also discuss an effective nested gradient flow algorithm for computing minimizers that controls the violation of the unit-length constraint. We present several simulations in 2D and 3D that document the performance of the proposed scheme and its ability to capture quite intriguing defects. This is joint work with Ricardo H. Nochetto (University of Maryland) and Shuo Yang (BIMSA).

Martin Stýblo (SIMONE Research Group s.r.o.)
2026-03-23 14:40 - 16:10
Title: The heart of industrial pipeline simulators - background, history, equations and numerical methods (https://master.researchseminars.org/talk/NSCM/212/)
by Martin Stýblo (SIMONE Research Group s.r.o.) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The lecture aims to illustrate the context of the pipeline simulation industry - underlying physics, governing equations, and numerical methods used by main packages. A brief overview of current research and possible future trends will be presented as well.

Jan Stebel (Technical University of Liberec)
2026-05-04 13:40 - 15:10
Title: Hydro-mechanical modelling of fractured porous media: Well-posedness and iterative schemes (https://master.researchseminars.org/talk/NSCM/213/)
by Jan Stebel (Technical University of Liberec) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Assessing the safety of deep geological repositories requires
rigorous modeling of coupled hydro-mechanical (HM) processes in fractured
crystalline rock. This involves addressing complex fracture manifolds where
mechanical deformation and fluid flow are linked by non-linear, mutually
dependent transmission conditions.
We present a mathematical framework for a non-linear HM model incorporating
fracture-matrix interactions, non-penetration contact conditions, and
aperture-dependent permeability. To solve the resulting evolution problem,
we employ the Rothe method for time discretization combined with a
fixed-stress iterative splitting scheme. We establish the well-posedness of
the formulation, identifying the stability conditions and structural
assumptions necessary to guarantee the existence of weak solutions. These
theoretical bounds further serve as the foundation for the convergence
analysis of the coupled FEM-MHFEM discretization. Numerical experiments are
presented to validate the theoretical results and demonstrate the solver's
robustness in complex geometries.

Jakub Cach (Charles University)
2026-05-11 13:40 - 15:10
Title: On bifurcations and traction forces on an obstacle in incompressible flow (https://master.researchseminars.org/talk/NSCM/214/)
by Jakub Cach (Charles University) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
We present a numerical study of flow-regime transitions in the two‑dimensional incompressible Navier--Stokes flow past a confined cylinder, focusing on Reynolds numbers up to 1000 within the Schäfer--Turek benchmark. For a fixed geometry, we observe a clear empirical correspondence between qualitative changes in steady boundary traction profiles, defined as the pointwise force density induced by the Cauchy stress tensor on the obstacle boundary, and bifurcations in the long‑time behavior of the unsteady flow. The observed transitions include onset of time‑periodic oscillations, secondary modifications of the oscillatory wake, emergence of pronounced asymmetry and the appearance of multiple steady solutions. These results indicate that steady traction profiles on the obstacle provide a sensitive diagnostic of critical Reynolds numbers at which qualitative changes in the global flow dynamics occur.

Mariya Ptashnyk (Heriot-Watt University Edinburgh)
2026-03-30 13:40 - 15:10
Title: Multiscale modelling, analysis and simulation of plant biomechanics and growth (https://master.researchseminars.org/talk/NSCM/215/)
by Mariya Ptashnyk (Heriot-Watt University Edinburgh) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The interplay between the complex microscopic structures and microscopic (cellular) processes enables many biological tissues to combine the ability to resist high pressure and mechanical forces with the flexibility required for large expansions and growth. To analyse the interactions between the mechanics, microscopic structure, and the chemistry we derive microscopic models for plant biomechanics, assuming that the elastic/viscoelastic properties of plant cell walls depend on the chemical processes and chemical reactions depend on the mechanical stresses. Multiplicative decomposition of the deformation gradient into elastic and growth parts is used to model the stress or strain-based growth. To analyse and simulate the complex multiscale models, the macroscopic effective equations are derived using homogenization techniques. Numerical solutions for the macroscopic models demonstrate the impact of the microscopic structure and tissue heterogeneity on deformation and growth.

Tomáš Bodnár (Department of Technical Mathematics, Czech Technical University in Prague)
2026-03-02 14:40 - 16:10
Title: Numerical simulations of hemodynamics and hemolysis (https://master.researchseminars.org/talk/NSCM/216/)
by Tomáš Bodnár (Department of Technical Mathematics, Czech Technical University in Prague) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
The development of blood contacting devices, such as Ventricular Assist Devices (VAD) became one of the most challenging tasks in modern bioengineering. The models of blood rheology, stress- and strain- based models of hemolysis, models of turbulence need to be solved at high resolution in complex geometries. The talk will present an overview of our current work in design of computational test case for VAD development and some of the recent results on combining the models of viscoelastic rheology with strain based models of hemolysis. This is a part of an ongoing joint work with Anna Lancmanova, Nico Dirkes, Alberto Girelli, Adelia Sequeira and Giulia Giantesio.

Nico Dirkes (RWTH Aachen)
2026-06-22 11:00 - 12:30
Title: Computational Prediction of Red Blood Cell Damage: Mathematical Modeling and Uncertainty Quantification (https://master.researchseminars.org/talk/NSCM/217/)
by Nico Dirkes (RWTH Aachen) as part of Nečas Seminar on Continuum Mechanics

Lecture held in Room K6, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..

Abstract
Computational simulations have become an important tool for the design of mechanical circulatory support devices as well as surgical planning ahead of implantation. While computational fluid dynamics can accurately predict flow fields, the prediction of hemolysis (red blood cell damage) remains challenging. Absolute predictions of hemolysis indices often deviate by multiple orders of magnitude from experimental measurements. This discrepancy can be attributed to two issues. First, most existing models for hemolysis employ a simple power law relationship between shear stress, exposure time, and hemolysis index, with model parameters fitted to experimental data. Second, experimental data often exhibits large variability between donors and between studies, leading to significant uncertainty in the fitted model parameters. This is due to individual differences in red blood cell properties and high sensitivity to experimental conditions. Consequently, the predictive capabilities of these models are limited, especially when applied to flow conditions that differ from those used in experiments.

We propose a two-sided approach to enhance the predictive capabilities of hemolysis models. First, we introduce a more physiological model that incorporates two important effects of the red blood cell membrane: viscoelastic deformation and pore formation. We highlight the differences between the Lagrangian and Eulerian model formulations. The Eulerian formulation enables a stabilized finite element discretization, which we apply to various benchmark cases. Second, we show how uncertainty quantification techniques can be employed to account for the variability in experimental data when fitting model parameters. This facilitates the integration of new experimental data as it becomes available, thereby enabling patient-specific predictions of hemolysis. Overall, this two-sided approach allows for more accurate and uncertainty-aware predictions of hemolysis to support the development process of future generations of biomedical devices.

Note that we meet in the lecture hall K6.

summer break
2026-06-29 13:40 - 15:10 | https://www.youtube.com/channel/UCn9vmevniyXXLEr7VBp5cCQ
Title: We will meet in October 2026 (https://master.researchseminars.org/talk/NSCM/218/)
by summer break as part of Nečas Seminar on Continuum Mechanics

Interactive livestream: https://cesnet.zoom.us/j/94319936814?pwd=[REDACTED]
View-only livestream: https://www.youtube.com/channel/UCn9vmevniyXXLEr7VBp5cCQ
Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA

Ulisse Stefanelli
2026-11-23 14:40 - 16:10 | https://www.youtube.com/channel/UCn9vmevniyXXLEr7VBp5cCQ
by Ulisse Stefanelli as part of Nečas Seminar on Continuum Mechanics

Interactive livestream: https://cesnet.zoom.us/j/94319936814?pwd=[REDACTED]
View-only livestream: https://www.youtube.com/channel/UCn9vmevniyXXLEr7VBp5cCQ
Lecture held in Room K3, Faculty of Mathematics and Physics, Charles University, Sokolovská 83 Prague 8..
Abstract: TBA
