NEČAS SEMINAR ON CONTINUUM MECHANICS
organized by the Mathematical Institute of the Charles University
each Monday at 15:40
in the MFF UK building,
Sokolovská 83, lecture room K1, 2^{nd}
floor,
proceeds with the following presentations:

15:40  Doc. RNDr. Petr Chvosta, CSc. (Katedra makromolekularni fyziky, MFF UK):  Matematika a fyzika Brownova sveta  Abstract: Jedna se o neformalni uvodni seznameni se soucasnym teoretickym vyzkumem fyzikalnich jevu na urovni reality, ktera se rozprostira na pomezi makrosveta a mikrosveta. V prednasce budou zdurazneny specificke dynamicke a energeticke principy Brownova sveta a nektere jejich neintuitivni dusledky. Adekvatnim matematickym nastrojem se zde jevi teorie stochastickych procesu, specialne teorie difuze a s ni souvisejici FokkerPlanckova rovnice. Diskuze se dotyka nove interpretace druhe hlavni vety termodynamiky a vyzaduje, mimo jine, revizi zakladnich termodynamickych pojmu jako jsou entropie, teplo a prace. Jednim z cilu zakladniho vyzkumu je navrzeni novych principu transformace vsudypritomneho termalniho pohybu na usmerneny makroskopicky pohyb. Takove tzv. Brownovy motory, tj. mechanismy hrajici v mezoskopicke oblasti roli znameho makroskopickeho Carnotova tepelneho stroje, priroda jiz patrne davno objevila a vyuziva je napriklad pri vnitrobunecnem transportu. 



15:40  
V case seminare od 16:00 se kona prednaska Dr. Karla Janecka, RSJ algorithmic trading.  Abstract: Prednasku organizuje SIAM SC a kona se v ramci oslav 60. vyroci MFF UK.
[viz. informacni letak] 



15:40  (MU UK):  Models of adhesive contacts delaminating at mixity modes  Abstract: After introducing a basic concept of quasistatic rateindependent adhesive contacts and surveying some results about it, a refinement by reflection of the mode of delamination will be exposed. As a matter of fact, engineering models distinguishes Mode I (=opening, with rather small activation energy needed) from Mode II (=shearing, with usually much bigger activation energy). Mixity mode combining both modes occurs most typically, rather than a pure Mode I or II. Some mixitysensitive models bear rigorous mathematical and numerical analysis. Twodimensional computational experiments will be presented, too. Eventually, some ratedependent effects like healing or viscosity or inertia will be mentioned. The presentation will reflect collaboration with L.Freddi, M.Kruzik, A.Mielke, V.Mantic, R.Paroni, R.Rossi, L.Scardia, M.Thomas, and C.Zanini, including computational simulations from M.Kocvara, C.G.Panagiotopoulos, R.Vodicka, J.Zeman. 



15:40  Prof. Dr. ClausDieter Munz (Institut fur Aerodynamik und Gasdynamik, Universitat Stuttgart):  Discontinuous Galerkin schemes with reconstruction  Abstract: Reconstruction is usually thought of a building block in volume schemes, but may also be combined with discontinuous Galerkin (DG) schemes. In this approach, the degrees of freedom of a piecewise polynomial approximation of degree N are directly based on the DG variational formulation, while reconstruction is used to raise the polynomial degree of the approximation to M>N and thus increase the order of accuracy of the solution. In this talk, I will give an overview of reconstructed DG schemes with an explicit time discretization. Within an implicit treatment of time I propose the use of reconstruction to estimate the local discretization error of a steady state DG solution.
An iterated defect correction is then applied to improve the accuracy of the steady solution.Within this approach one only needs the inversion of the basic lowerorder DG scheme. The main advantage is that the defect correction does not affect the DG scheme beside a modication of the right hand side, and the matrix of the linear system to be solved remains unchanged. Due to the fact that computational effort for higher order schemes strongly increases with the order the defect correction scheme may be considerably more efficient. Numerical results for Euler and NavierStokes equations are shown. 



15:40  Prof. Endre Suli (Mathematical Institute, University of Oxford):  Existence of global weak solutions to kinetic models of nonhomogeneous dilute polymeric fluids  Abstract: We prove the existence of globalintime weak solutions to a general
class of coupled beadspring chain models that arise from the kinetic
theory of dilute solutions of nonhomogeneous polymeric liquids with
noninteracting polymer chains, with finitely extensible nonlinear
elastic spring potentials. The class of models under consideration
involves the unsteady incompressible NavierStokes equations with
variable density and densitydependent dynamic
viscosity in a bounded domain in two or three space dimensions for the
density, the velocity and the pressure of the fluid, with an elastic
extrastress tensor appearing on the righthand side in the momentum
equation. The extrastress tensor stems from the random movement of the
polymer chains and is defined by the Kramers expression through the
associated probability density function that satisfies a
FokkerPlancktype parabolic equation, a crucial feature of which is
the presence of a centreofmass diffusion term and a nonlinear
densitydependent drag coefficient. 



15:40  prof. Tarak Ben Zineb (LEMTA, Lorraine University, CNRS, Francie):  A constitutive model for Febased SMA considering martensitic transformation and plastic sliding coupling: Application to finite element structural analysis  Abstract: In this paper, a finiteelement numerical tool adapted to Febased SMA structural analysis is proposed. The algorithm is based on an earlier developed constitutive model which describes the effect of phase transformation, plastic sliding and their interactions on the thermomechanical behavior. This model was derived from an assumed expression of the Gibbs free energy taking non linear interaction of quantities related to inter and intragranular incompatibilities as well as interaction of mechanical and chemical quantities into account. Two scalar internal variables were considered to describe the phase transformation and plastic sliding effects. The hysteretic and specific behavior patterns of Febased SMA during reverse transformation were studied by assuming a dissipation expression. The proposed model effectively describes complex thermomechanical loading paths. The numerical tool derived from the implicit resolution of the non linear partial derivative constitutive equations was implemented into the Abaqus finite element code via the UMAT subroutine. After tests to verify the homogeneous and heterogeneous thermomechanical loading, an example of Febased SMA application was studied which corresponded to an Febased SMA tightening system made up of fish plates for crane rails. The results we obtained were compared to experimental ones. 



15:40   A thermodynamical framework for chemically reacting systems  Abstract: In this talk I present a very general thermodynamic framework that is capable of describing a large class of bodies undergoing entropy producing processes. Attention will be focused on bodies that are undergoing chemical reactions and the framework takes stoichiometry into account. As a special subcase, we describe the response of viscoelastic materials that undergo chemical reactions. One of the quintessential features of this framework is that the second law of thermodynamics is formulated by introducing the Gibbs potential, which is the natural way to study problems involving chemical reactions. The Gibbs potentialbased formulation also naturally leads to implicit constitutive equations for the stress tensor. The assumption of maximization of the rate of entropy production due to dissipation, heat conduction, and chemical reactions is invoked to determine an equation for the evolution of the natural configuration, the heat flux vector and a new set of equations for the evolution of the concentration of the chemical constituents. To determine the efficacy of the framework with regard to chemical reactions we consider the reactions occurring during vulcanization of rubber. The theoretically predicted distribution of mono,di and polysulfidic crosslinks by using the framework agree reasonably well with available experimental data. 



15:40  Mgr. Jan Stebel, PhD (NTI FM TU Liberec):  Numerical solution of Stokes problem and of its generalization within implicit constitutive theory  Abstract: Rheology of some classes of nonNewtonian fluids is characterized by
an implicit relation of the Cauchy stress and the symmetric velocity
gradient. This leads to a generalized Stokes problem in which the
stress becomes an independent unknown and the constitutive relation
plays the role of an additional constraint. For successfull numerical
solution it is crucial to find stable finite elements that take into
account the twofold saddlepoint structure of the problem. I will
describe several formulations of the generalized Stokes problem,
discuss the choice of finite element spaces and present some numerical
results. 



15:40  Prof. Dr. Ing. Eduard Rohan (Fakulta aplikovanych ved, Katedra mechaniky, ZCU):  Modeling double porosity media using hierarchical homogenization  Abstract: Models of fluid saturated porous media (FSPM) are widely used in geomechanics, civil engineering and biomechanics; in the last application, FSPM models can approximate bone mechanics, or tissue perfusion, to name a few examples. Asymptotic analysis of PDEs with strongly oscillating coefficients forms a mathematically sound basis for modeling complicated interactions in heterogeneous materials with respect to their microstructure. Assuming scale separation, this approach can be adapted for simultaneous modeling of materials on the micro, meso and macroscopic scales. In the lecture, various models of FSPM will be presented which were obtained using hierarchical homogenization, or using homogenization of PDEs with scaledependent coefficients. Also different origins of the fading memory effects observed at the macroscopic scale will be discussed. 



15:40  Mgr. Stanislav Sysala, Ph.D. (Institute of Geonics AS CR, v.v.i., Applied mathematics and computer science):  Preliminary modelling of rock pillar failure processes based on continuum mechanics  Abstract: Firstly, we briefly describe the Aspo Pillar Stability Experiment (APSE). The APSE experiment was carried out to examine the failure process in a heterogeneous and slightly fractured granite rock mass when subjected to coupled excavationinduced and thermalinduced stresses. The APSE experiment has been related to an underground nuclear waste repository research. Secondly, we map the pillar failure process and describe some effects that were observed during the process or influenced it. Thirdly, we briefly inform about investigation based on 3D thermoelastic modelling. Fourthly, we introduce simplied 2D models representing a crosssection of the pillar. The models geometry and loading path correspond with the previous 3D thermoelastic modelling. We consider three preliminary continual approaches elastic, perfect elastoplastic and a combination of perfect elastoplasticity and continuum damage mechanics. We discuss advantages and disadvantages of the approaches from mathematical and experimental points of view. We also introduce a simple coupling of the models with thermal loading. Fifthly, we mention few comments to implementation of the problems. Sixthly, we perform few numerical experiments to investigate stability of the models or to describe which of the investigated effects can be described by the models or not. 



15:40  Doc. Dr. rer. nat. Ing. Jan Valdman (VSBTU Ostrava):  Multisurface elastoplastic continuum  modeling and computations  Abstract: The quasistatic evolution of an elastoplastic body with a multisurface constitutive law of linear kinematic hardening type
allows the modeling of curved stressstrain relations. It generalizes classical smallstrain elastoplasticity from one to various plastic phases. We presents the mathematical model, existence and uniqueness of the solution of the corresponding initialboundary value problem and numerical computation using finite elements. The talk is based on PhD thesis of Jan Valdman from 2002 and later joint journal publications with M. Brokate, C. Carstensen and A. Hofinger. 



15:40  Privatdozent Dr. Dirk Pauly (Universitat DuisburgEssen, Fakultat fur Mathematik):  Poincare meets Korn via Maxwell: Extending Korn s First Inequality to Incompatible Tensor Fields  



10:00  Prof. Zdeňek Bažant (Northwestern University, Evanston, Illinois, USA):  Energy Conservation Errors of Objective Stress Rates in ABAQUS, ANSYS, LSDYNA and Other FE Codes: Their Magnitude and How to Correct Them  Abstract: PDF file
Please notice different date and place: on Thursday, September 27, in Ústav termomechaniky (lecture room B), Dolejškova 5, Praha 8. 



15:40  (School of Mechanical Engineering, Tel Aviv University, Israel):  Numerical modeling of instabilities of confined flows: concepts, achievements, benchmarks and comparison with experiment  Abstract: This is a review lecture describing recent achievements in computational modelling of threedimensional instabilities of flows in closed containers. The study is motivated by melt instabilities in bulk crystal growth processes and requires consideration of rather complicated domains, as well as accounting for different nonlinear phenomena, e.g., phase change and radiation. This makes it impossible to apply spectral or pseudospectral methods, which were traditionally used for solution of model stability problems. Lowerorder methods, which are more flexible but converge slower, become the choice. We discuss how a numerical process containing a direct solver for calculation of a developed steady flow and an eigenvalue solver needed for the stability analysis should be treated. The first question addressed in this study is how fine should be a finite volume grid to yield converged critical parameters corresponding to the primary instability of a developed flow. For this purpose we consider a series of model problems which includes also some wellknown benchmarks. The second issue is the comparison of numerical results with the existing experimental data, which yields the most important validation of a numerical code. We discuss also results of parametric stability studies for some model configurations and describe effects of stabilization and destabilization of flows by different combinations of heating and rotation. 



15:40  (Weierstrass Institute, Berlin):  On the structure of the quasiconvex hull in planar elasticity  Abstract: We study quasiconvexity in the calculus of variations, in particular, quasiconvexity for sets of matrices. Let K and L be compact sets of real 2x2 matrices with positive determinant. Suppose that both sets are frame invariant, meaning invariant under the left action of the special orthogonal group. Then we give an algebraic condition for K and L to be incompatible for microstructures. This result permits a simplified characterization of the quasiconvex hull and the rankone convex hull in
planar elasticity.
At the beginning of the talk, there will be a short motivation and an introduction to quasiconvexity. 



15:40  Ing. Vaclav Klika, Ph.D. and Prof. Frantisek Marsik (KM, FJFI CVUT and Institute of Thermomechanics, AV CR):  Nonequilibrium thermodynamics and bone tissue remodelling  Abstract: Motivated by biological applications and a great debate in literature (e.g. in bone tissue development and regeneration) about the significance of mechanochemical coupling and the nature of these quantities, we try to pursue this problem from thermodynamical point of view.
First, we shall discuss the use of nonequilibrium thermodynamics, classical irreversible thermodynamics, for extensions of Law of Mass Action that is frequently used in chemical kinetics. Such extensions enable to study the effects and nature of mechanochemical coupling.
Further, within GENERIC framework we propose a thermodynamically consistent way (or ways) of capturing a nonlinear coupling between scalar quantities, namely affinities and scalar mechanical quantities. A modified version of the law of mass action is obtained which reflects the coupling effects by modification of reaction constants.
The results from nonlinear coupling shall be discussed with CIT predictions. Also a means of comparison of the effects of different types of already recognised mechanical stimulation shall be given.As an illustrative example we shall apply the theoretical findings to model bone remodelling process. 



15:40  prof. RNDr. Miloslav Feistauer, DrSc., Dr.h.c. (KNM, MFF UK):  Numerical simulation of interaction of compressible flow with elastic structures  



15:40  RNDr. Jiri Kroc, Ph.D.  Introduction To Dynamic Recrystallization And Structural Design Based On Complex Systems: Building Vocabulary  Abstract: Complex systems (CSs) represent a vital, productive, fast growing theory with applications in all scientific fields. Today, we briefly encounter development of CSs accompanied by carefully selected applications explaining their power. CSs are often called as postNewtonian scientific approach because they do not work with the concept of equations. Instead of equations, CSs employ a vast number of identical copies of units (just of several generic types), representing the bottomlevel of the system, which are mutually interacting on this bottomlevel. The toplevel behavior resulting from mutual interactions of the bottomlevel units is not encoded, as e.g. in ant colony created through interactions of ants. The theory of cellular automata, which are
firmly sitting within the core of modeling of CSs, is reviewed. The concept of selforganization and emergence and ideas behind it are briefly demonstrated.
The main attention of this talk is focused to presentation of novel CSs approaches employed in models of dynamic recrystallization (DRX) and structural design. In DRX, experimental observations are reviewed and followed by historical development of models of DRX which is demonstrated on two presented models (discrete and continuous). In structural design, models based on cellular automata formulation of elastic or plastic deformations of constructions subjected to static or dynamic load are reviewed. The case of truss bridge is shown in detail. This enables us to optimize shape, weight, internal structure, etc., against desired properties of the final product. Such computationally supported design of not only mechanical components and constructions c
an leads to a substantial increase of their performance. 



15:40  prof. Didier Henrion (LAASCNRS Univ. Toulouse and FELCVUT Prague):  Continuity equations on measures and semidefinite programming for polynomial control systems  Abstract: Following original ideas of Liouville (1838), Poincare (1899), Carleman (1932), KryloffBogoliouboff (1937) and L. C. Young (1969), many nonconvex nonlinear infinitedimensional optimization problems can be reformulated into convex linear programming (LP) problems in a Banach space of measures. Recent developments in functional analysis and real algebraic geometry can be exploited to solve numerically these measure LPs with the help of semidefinite programming (SDP), via a converging hierarchy of finitedimensional LPs in the cone of positive semidefinite matrices. In this talk we apply these techniques to solve the problem of estimating the region of attraction of controlled ODEs with polynomial vector field and semialgebraic state and control constraints. We first reformulate this problem as an conic Banach LP involving the Liouville continuity (advection) PDE on occupation measures. Then we apply our hierarchy of SDP problems to generate nested semialgebraic outer approximations converging almost uniformly to the region of attraction. 



15:40  Prof. K.R. Rajagopal, DrHC (Mechanical Engineering, Texas A&M University, College Station):  Modeling fracture in brittle solids  



15:40  Petr Filip, CSc. (Institute of Hydrodynamics, ASCR):  Similar and quasisimilar solutions for flows of Newtonian and nonNewtonian fluids  Abstract: A similarity solution of the swirling radial jet is derived including an interpretation of circumferencepointsource. The solution is applied to a description of velocity field in socalled rotor region in a mixing vessel when a Rushtontype impeller is used. The parameters obtained during the similarity procedure are matched with the parameters describing mixing conditions.
Helical steady state, laminar, isothermal flow of incompressible powerlaw fluids through a concentric annulus is analysed for a stationary outer cylinder with the inner pipe rotating with constant torque. Pressure is applied in an axial direction. Using dimensionless analysis, a quasisimilarity solution is derived for a sufficiently broad region of rheological, geometrical and dynamical parameters. This solution provides functional dependence of flow rate on an aspect ratio of the innertoouter cylinders, parameters in the powerlaw rheological model, and torque. 



15:40  Mgr. Petra Pustejovska, Ph.D. (Institute of Computational Mathematics, TU Graz):  Modeling of blood flow in real geometry aneurysm  



15:40  Dr. Giuseppe Tomassetti (Dipt. Ingegneria Civile, Universita di Roma `Tor Vergata):  Modeling hydrogen transport and phase transformation in metallic solids  Abstract: A continuum theory coupling diffusion, phase transformation,
and deformation in solids under large strains will be presented,
and possible applications to the modeling of hydrogen storage
in metallic compounds will be discussed and mathematical analysis will briefly be outlined, too. 



15:40  
15:45  doc. RNDr. Oldrich John, CSc. (Dept. of Math. Anal., Math.Phys. Faculty, Charles Univ.):  Jindrich Necas a regularita  nekolik vzpominek  

16:00  RNDr. Miroslav Bulicek, Ph.D. (Math. Inst., Charles Univ.):  On recent progress in the regularity theory for minimizers of variational integrals  Abstract: The 19th Hilbert problem asks whether minimizers of a regular
variational problem are analytic. In 60s, E.DeGiorgi and J.Nash proved that this hypothesis is true in the scalar case. On the other hand, in the vectorial case the hypothesis is not true, as was shown by J.Necas (1975), who found a variational problem whose minimizer is Lipschitz continuous but not better. Moreover, it was shown by V.Sverak and X.Yan (2000), that some minimizers can even
be discontinuous and unbounded. Therefore, it is of a real interest to identify a nontrivial class of vectorial variational problems that admit smooth or at least Holder continuous minimizers. First such result is due to the Uhlenbeck (1977) who found a very special class for which the minimizer is smooth. In last decades, a lot of extensions of the Uhlenbeck result was proved for various types of variational problems but only under the very restrictive assumptions which are, in fact, not far from the Uhlenbeck setting.
In this talk, a new, much more general class of variational problems for which it is possible to prove the Holder continuity of the minimizer will be presented. Moreover, it will be seen that the convexity of the potential in fact does not play any role, and revealed much more importance of a structural condition, which
in our case can read as a splitting condition. 



15:40  Mgr. J. Stebel, Ph.D. jointly with Prof.RNDr. J.Haslinger, DrSc. (Math. Institute of the ASCR & Dept. of Numer. Math., Charles Univ.):  Shape optimization in Stokes problems with threshold slip boundary conditions  Abstract: We study the Stokes problems in a bounded planar domain Omega with a
frictiontype boundary condition that switches between a slip and noslip stage. Our main goal is to determine under which conditions concerning smoothness of Omega, solutions to the Stokes system with the slip boundary conditions depend continuously on variations of Omega. Having this result at our disposal, we easily prove the existence of a solution to optimal shape design problems for a large class of cost functionals. In order to
release the impermeability condition, whose numerical treatment could be troublesome, we use a penalty approach. We introduce a family of shape optimization problems with the penalized state relations. Finally we establish convergence properties between solutions to the original and modified shape optimization problems when the penalty parameter tends to zero. 


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