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Liste des exposés

I. Nouvelles tendances en mécanique des fluides

II. Problèmes à frontière libre

III. Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus

IV. Processus stochastiques

V. Maths et planète Terre

VI. Analyse et contrôle des EDP

VII. Statistiques

VIII. Analyse non-lisse et optimisation

Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus

(cette liste est en processus d'actualisation)

List des exposés

1.
(CLEJA)-TIGOIU Sanda
Faculty of Mathematics and Computer Science, University of Bucharest, Bucharest
Titre: Continuous model of structural defects in finite elasto-plasticity (details)
Résumé:
Continuous defects in crystaline materials are mathematically described in terms of incompatibilities of the so-called „plastic distortion” and „plastic connection”. From physical point of view the micro-forces (micro stresses and micro momenta), which are power conjugated with the appropriate rates of defects, generate the dissipation of the internal power and satisfy their own balance equations. The dissipative evolution equations for geometrical measures of defects are derived to be compatible with the principle of the free energy imbalance. Appropriate boundary value problems have been provided by coupling the balance equations for macro-forces and evolution equations for defects. The initial conditions correpond to given initial defects (for instance a set of dipoles of disclinations).
2.
Institut de Mathématiques de l’Académie Roumaine, Roumanie
Titre: Méthode multigrille pour les inégalités contenant un terme non-différentiable (details)
Résumé:
\begin{abstract} Au d\'ebut, nous introduisons et prouvons la convergence globale de certaines m\'ethodes multiniveaux et multigrilles pour les in\'egalit\'es variationnelles (de la premi\ere esp\'ece). Les m\'ethodes sont introduites comme des algorithmes de correction sur les sousespaces dans un espace de Banach r\'eflexif, o\u de r\'esultats g\'en\'eraux de convergence sont d\'eriv\'es. Ces algorithmes deviennent des m\'ethodes multigrille et multiniveaux en introduisant les espaces d'\'el\'ements finis. Dans ce cas, les taux globaux de convergence sont \'ecrits en fonction du nombre de niveaux. Une extension directe de ces m\'ethodes aux in\'egalit\'es variationnelles de la deuxi\eme esp\'ece et aux in\'egalit\'es quasi-variationnelles n'est pas tr\es \'evidente, mais pour eux, nous pouvons introduire certaines m\'ethodes multigrilles qui sont bas\'ees sur celles pr\'ec\'edement d\'ecrites. En utilisant des lin\'earisations de Newton de la fonctionnelle non-diff\'erentiable, R. Kornhuber a introduit des m\'ethodes multigrilles pour les probl\emes de compl\'ementarit\'e et a estim\'e leur taux de convergence asymptotique. Dans cet expos\'e, nous estimons le taux de convergence globale d'une m\'ethode multigrille pour le cas particulier des in\'egalit\'es quasi-variationnelle lorsque l'in\'egalit\'e contient un terme donn\'e par un op\'erateur de contraction. En outre, nous introduisons un algorithme multigrille pour les in\'egalit\'es variationnelles de la deuxi\eme esp\'ece bas\'e sur la r\'egularisation de Moreau du terme non-diff\'erentiable de l'in\'egalit\'e. De cette fa\c con, nous obtenons une in\'egalit\'e variationnelle de la premi\ere esp\ece. Nous montrons que la solution du probl\eme r\'egularis\'e converge vers la solution du probl\eme initial et pour le r\'esoudre, nous consid\'erons la m\'ethode multigrille d\'ej\a \'etudi\'e. Les exp\'eriences num\'eriques ont montr\'e une tr\es bonne convergence de la m\'ethode, m\^eme pour de valeurs du param\`etre de r\'egularisation proches de z\'ero. \end{abstract}
3.
BUCUR Andreea- Valentina
Alexandru Ioan Cuza University of Iasi, Romania
Titre: Spatial behavior in linear theory of thermoviscoelasticity backward in time for porous media (details)
Résumé:
In this presentation we study the spatial behavior of the solutions to the backward in time problem associated with the linear theory of thermoviscoelastic materials with voids. We associate with a solution of the considered problem an appropriate time-weighted volume measure. In terms of such measure we establish a first order partial differential inequality, and it is further shown how the inequality implies the spatial exponential decay of the porous thermoviscoelastic process backward in time.
4.
CHIRITA Stan
Universitatea Alexandru Ioan Cuza din Iasi, Romania
Titre: On the three-phase-lag model of heat conduction (details)
Résumé:
This contribution studies the time differential three-phase-lag heat conduction model. The model is reformulated by means of the fading memory theory in which the heat flux vector depends on the history of the thermal displacement gradient and then the thermodynamic principles are applied to obtain the restrictions upon the delay times. Under the thermodynamic restrictions just obtained, the continuous dependence of solutions with respect to the given initial data and the supply term is established for the related initial boundary value problems.
5.
CRACIUN Eduard - Marius
"Ovidius" University of Constanta, Romania
Titre: Mathematical Modeling of Interface Cracks in Fiber Reinforced Elastic Composites (details)
Résumé:
\documentclass[11pt, a4paper]{article} \begin{document} \title{Mathematical Modeling of Interface Cracks in Fiber Reinforced Elastic Composites} \author{$$E. M. Craciun$$ \\ $$^1$$Ovidius University of Constanta, Romania} \date{} \maketitle A pre-stressed fiber reinforced elastic composite containing an interface crack in all three modes of classical fracture is studied. We consider the representation of the incremental fields for our initial deformed elastic composite, due to Guz and Soos. We formulate and solve the interface crack mathematical problem for all three modes of classical fracture, using a model of zero thickness linear interface. Using the boundary conditions of the interface crack in the pre-stressed elastic composite material, we solve the homogeneous and a nonhomogeneous Riemann - Hilbert problems. A nonhomogeneous linear complex differential equation having the unknown complex potential is obtained. We get the complex potentials, corresponding to each mode of the classical fracture. The incremental displacement and stress fields in the vicinity of the crack field are obtained using the complex potentials and the representation formulae.\\ The interaction of collinear interface cracks in the pre-stressed elastic composite is considered. \end{document}
6.
DANESCU Alexandre
Ecole Centrale de Lyon, France
Titre: Mindlin model as an exact interpolation of the chain with hyper-pre-stress (details)
Résumé:
In this talk we shall discuss the role of null-lagrangians for the exact interpolation of the elastic chain with hyper-pre-stress. We show that the second-graident of strain model of Mindlin and null-lagrangians are the minimum requirements for the exact interpolation.
7.
DUMONT Serge
UNimes/IMAG Montpellier, France
Titre: Active Set Method for solving Multi-Contact Problems (details)
Résumé:
In this presentation, an active set method is developed in the context of the Discrete Element Method, where a frictional contact of Coulomb type between a collection of rigid bodies is considered. The new method, which takes his advantage in the simplicity of implementation, is compared with more classical ones, such as Augmented Lagrangian method and bi-potential method. Numerical results are provided in order to compare various methods, both in terms of time computing and of qualitative properties of the numerical solutions.
8.
FACIU Cristian
Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania
Titre: Modeling temporal and spatial instabilities of the Portevin - Le Chatelier effect (details)
Résumé:
The Portevin-Le Chatelier (PLC) effect is an unstable, oscillatory plastic flow that may be observed in metallic alloys subjected to load-or displacement-controlled deformation. Physically it is explained by the dynamic strain ageing as a micro mechanism of plastic instability phenomena due to dislocation–solute and dislocation–dislocation interactions. An elastic-viscoplastic model of McCormick type incorporating dynamic strain ageing and negative strain-rate sensitivity is considered. Critical conditions on the material parameters for the emergence of spatial instability and localization phenomena for the PLC effect are investigated.
9.
GALES Catalin
AL. I. Cuza University of Iasi, Romania
Titre: Resonance effects in the dynamics of space debris (details)
Résumé:
The dynamics of small bodies around the Earth has gained a renewed interest, since the awareness of the problems that space debris can cause in the nearby future. A relevant role in the dynamics of space debris is played by resonances. Two types of resonance affect the motion of space debris: tesseral resonances, occurring when there is a commensurability between the Earth's rotation period and the orbital period of the space debris, and lunisolar resonances, which involve commensurabilities among the slow frequencies of orbital precession of the debris and the perturbing body. Tesseral resonances provoke variations of the semi--major axis on a time scale of the order of hundreds of days, while lunisolar resonances influence the evolution of the eccentricity and inclination on a much longer time scale, of the order of tens (or hundreds) of years. The purpose of this talk is to describe some results obtained recently by using tools of the perturbation theory of Hamiltonian systems.
10.
GARAJEU Mihail
Aix-Marseille Université, FRANCE
Titre: Solutions exactes d’une sphère composite viscoélastique non linéaire sous chargement isotrope (details)
Résumé:
Dans cette étude, une approche multi-échelle est dévelopée pour comprendre et prédire l'effet du plutonium sur le comportement effectif du combustible MOX, utilisé dans les réacteurs à eau préssurisée. Le combustible MOX est un composite triphasé, constitué d'une phase matricielle à teneur modérée en plutonium dans laquelle sont réparties des particules combustibles. Ces dernières sont composées d'amas plutonifières à forte concentration en plutonium et d'amas uranifières à faible proportion en plutonium. Les phases inclusionnaires étant proches d'une géométrie sphérique, la microstructure du combustible MOX peut etre modélisée par l'assemblage des sphères composites de Hasin. Des solutions exactes pour des cas de chargement isotrope de relaxation sont obtenues. Dans le cas d'un chargement de fluage, la distribution spatiale de la contrainte équivalente est la solution d'une équation intégro-différentielle qui est résolue numériquement.
11.
GHIBA Ionel-dumitrel
Alexandru Ioan Cuza University of Ias; University Duisburg-Essen., Romania; Germany
Titre: On some Hencky-type energies (details)
Résumé:
The aim of this talk is to present properties of some functions depending on the isotropic invariants $$\|{\rm dev}_n \log U\|^2 (n = 2,3)$$ and $$[{\rm tr}(\log U)]^2$$ of the logarithmic strain tensor $$\log U$$. Here, $$F = \nabla \varphi$$ is the gradient of deformation, $$U=\sqrt{F^TF}$$ is the right stretch tensor and $${\rm dev}_n \log U$$ is the deviatoric part of the strain tensor $$\log U$$.
12.
IONESCU Ioan
Universtié Paris 13, Sorbonne Paris-Cité, France
Titre: MATERIAL INSTABILIES IN MODELING MULTISCALE ANISOTROPIC DAMAGE (details)
Résumé:
The used geometric damage model used here, represented by micro-cracks growing under dynamic or quasi- static loading, is able to describe the link between the micro and macro-scale damage mechanism. We give a stability analysis and we derive a stability criterion for dynamic and quasi-static processes. We show that that for a given con- tinuous strain history the quasi-static or dynamic problems are instable or ill-posed (multiplicity of material responses) and whatever the selection rule is adopted, shocks (time discontinuities) will occur. These stability criteria are used to analyse some special configurations: one family of micro-cracks in mode I, II and III and in plane strain or plain stress ; initial isotropic distribution and initial anisotropic distribution of micro-cracks. In each case we determine a critical crack density parameter and critical micro-crack radius (length) which distinguish between stable and unstable behaviors.
13.
KALITA Piotr
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland
Titre: Micropolar effects stabilize the flow for the Rayleigh--B\'{e}nard problem (details)
Résumé:
We study the problem of Rayleigh--B\'{e}nard convection in micropolar incompressible fluid in 2d. We compare the dynamics with the corresponding dynamics for the Newtonian fluid. Using a variant of the method of Constantin and Doering we obtain the estimates on the Nusselt number, which measures the heat fluxes due to convection. We demonstrate that convective heat fluxes are decreased in presence of micropolar effects. We also obtain the result on attractor bifurcation from globally asymptotically stable solution with no convection, to the attractor which contains the configurations at which the convection occurs. We prove that critical Rayleigh number at which this bifurcation occurs is higher in micropolar fluids than in Newtonian fluids. This is joint work with Jose A. Langa and Grzegorz Łukaszewicz.
14.
MALIN Maria
City University of Hong Kong, China (Hong Kong)
Titre: Nonlinear Korn inequalities on a surface: some new results (details)
Résumé:
As is well-known, a linear Korn inequality on a surface is an estimate of the distance between two surfaces in terms of the corresponding linearized change of metric and change of curvature tensors. We present here some nonlinear Korn inequalities on a surface, where the distance between two surfaces is now estimated in terms of the exact differences between their first and second fundamental forms, i.e., without any linearization or approximation. More specifically, we review some nonlinear Korn inequalities on a surface in Sobolev spaces which have been obtained in [1]. Likewise we show that, under appropriate additional assumptions, we can get rid of the third fundamental form found in [1]. [1]: P.G. Ciarlet, L. Gratie, C. Mardare: A nonlinear Korn inequality on a surface, J. Math. Pures Appl. 85 (2006), 2-16.
15.
MIGORSKI Stanislaw
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland
Titre: Variational-Hemivariational Inequality in Contact Problem for Locking Materials (details)
Résumé:
We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.
16.
NECIB Brahim
University of Constantine, Algeria
Titre: Analyse dynamique des structures bidimensionnelles planes par modélisation continue utilisant la méthode des éléments finis (details)
Résumé:
Les structures spatiales discrètes sont d’une grande importance dans le domaine d’application de l’aéronautique, la mécanique, le génie civil et l’aérospatiale. Leur analyse statique et dynamique est aussi importante pour leur assurer un bon dimensionnement et leur éviter la résonnance de vibration, la fissuration, la rupture et leur désastre due à des conditions extérieures durant leur fonctionnement et ainsi d’augmenter leur durée de vie. Ainsi leur analyse reste aussi complexe que la complexité de leur assemblages spécialement pour les structures spatiales bidimensionnelles vu leur dimensionnement, l’orientation de leurs éléments et leur condition aux limites. En effet, la méthode des éléments finis (M.E.F) est une nouvelle méthode utilisée pour analyser et calculer ces types de structures par modélisation durant un temps d’exécution minimum. Notre travail consiste en l’analyse statique et dynamique des structures mécaniques bidimensionnelles planes sous l’effet des excitations extérieures et sous différentes conditions aux limites en utilisant la méthode des éléments finis. Comme exemple d’application, une structure bidimensionnelle en charpente métallique est considérée. Les éléments de la structure sont modélisés comparativement par des éléments barres et des éléments poutres, interconnectés aux nœuds par soudage ou rivetage. Les matrices de masse et de rigidité de la structure sont déterminées respectivement par assemblage de tous les éléments. Les forces axiales dans chaque élément de la structure ont été calculées en fonction des efforts extérieurs appliqués sur la structure. Aussi les dix premières modes de vibration de la structure bidimensionnelle ont été déterminées et analysées en fonction de différentes condition aux limites.
17.
PASA Gelu
Simion Stoilow Institute of Mathematics of Romanian Academy, ROMANIA
Titre: On the 3D immiscible displacement in Hele-Shaw cells (details)
Résumé:
We study the linear stability of the displacement of two incompressible Stokes fluids in a 3D Hele - Shaw cell. The corresponding growth constant contains two new terms, compared with the Saffman-Taylor formula. For large enough surface tension on the interface, we get an almost stable displacement, even if the displacing fluid is less viscous. Moreover, if the surface tension on the interface is zero, then our growth rate is bounded in terms of the wavenumbers of the perturbations. These results are in contradiction with the classical Saffman-Taylor criterion. In the case of very small viscosity of the displacing fluid, we recall a previous formula related with the Laplace's law for a Stokes fluid displaced by air in a Hele-Shaw cell.
18.
PATRULESCU Flavius-olimpiu
Romanian Academy, "Tiberiu Popoviciu" Institute of Numerical Analysis, Romania
Titre: A regularization method for a viscoelastic contact problem (details)
Résumé:
We consider a mathematical model which describes the quasistatic contact between a viscoelastic body and a deformable obstacle, the so-called foundation. The material’s behavior is modelled with a viscoelastic constitutive law with long memory. The contact is frictionless and is modelled with a multivalued normal compliance condition. We present a regularization method in the study of a class of variational inequalities involving history-dependent operators. Finally, we turn back to our contact model and apply our abstract results in the study of this problem.
19.
SECK Mohamed El Bachir
Laboratoire de Mécanique et d'Aoustique ( LMA) , CEA cadarache, FRANCE
Titre: Solutions exactes d'une sphère composite viscoélastique non linéaire sous chargement isotrope (details)
Résumé:
Dans cette étude, une approche multi-échelle est dévelopée pour comprendre et prédire l'effet du plutonium sur le comportement effectif du combustible MOX, utilisé dans les réacteurs à eau préssurisée. Le combustible MOX est un composite triphasé, constitué d'une phase matricielle à teneur modérée en plutonium dans laquelle sont réparties des particules combustibles. Ces dernières sont composées d'amas plutonifières à forte concentration en plutonium et d'amas uranifières à faible proportion en plutonium. Les phases inclusionnaires étant proches d'une géométrie sphérique, la microstructure du combustible MOX peut etre modélisée par l'assemblage des sphères composites de Hasin. Des solutions exactes pour des cas de chargement isotrope de relaxation sont obtenues. Dans le cas d'un chargement de fluage, la distribution spatiale de la contrainte équivalente est la solution d'une équation intégro-différentielle qui est résolue numériquement.
20.
SLUZALEC Tomasz
Jagiellonian University in Krakow, Faculty of Mathematics and Computer Science, Poland
Titre: Theoretical and numerical approach for problem solving steady-state heat conduction (details)
Résumé:
Galerkin method is developed for a stationary variational-hemivariational inequality modeling problem in the steady-state heat conduction. The numerical convergence rate for some classes of thermal operators is presented. The problem is solved numerically by minimization of an associated energy functional. In order to find a solution of optimization problem we apply the Proximal Bundle Method.
21.
SOFONEA Mircea
University of Perpignan Via Domitia, France
Titre: Variational-Hemivariational Inequalities with Applications in Contact Mechanics (details)
Résumé:
We consider two classes of variational-hemivariational inequalities for which we establish existence and uniqueness results. The proofs are based on arguments of multivalued pseudomonotone operators and fixed point. Then, we introduce a penalty method and prove the unique solvability of the penalized problems together with the convergence of their solutions, as the the penalty parameter converges to zero. We apply these results results to variational-hemivariational inequalities arising in the study of static and quasistatic contact problems with elastic, viscoelastic and viscoplastic materials.
22.
TIGOIU Victor
Faculty of Mathematics and Computer Science, University of Bucharest, Romania
Titre: Continuous model of structural defects in finite elasto-plasticity (details)
Résumé:
Continuous defects in crystaline materials are mathematically described in terms of incompatibilities of the so-called „plastic distortion” and „plastic connection”. From physical point of view the micro-forces (micro stresses and micro momenta), which are power conjugated with the appropriate rates of defects, generate the dissipation of the internal power and satisfy their own balance equations. The dissipative evolution equations for geometrical measures of defects are derived to be compatible with the principle of the free energy imbalance. Appropriate boundary value problems have been provided by coupling the balance equations for macro-forces and evolution equations for defects. The initial conditions correpond to given initial defects (for instance a set of dipoles of disclinations).

Participants

1.
SECK Mohamed El Bachir
Laboratoire de Mécanique et d'Aoustique ( LMA) , CEA cadarache, FRANCE