Finite difference/finite elements methods for transient/stationary diffusion/thermal problems; finite elements method for linear/non-linear problems; finite elements method for coupled problems: poroelasticity, elasticity/diffusion coupling.

Phenomenological aspects for damage modeling. Damage variables. Effective stresses. Damage measures. Elementary laws and damage criterion; Thermodynamic formulation. Dimensional representation of damage. Isotropic and anisotropic damage theories; Specific models. Plastic ductile damage. Creep damage. Fatigue damage. Interaction effects; Deformation/damage coupling. Elasticity(resp. Plasticity)/Damage coupling; Application to the modeling the behavior of concrete. Behavior in tensile and compression. Relationship between damage and anelastic strains. Strain localization.

1) External acoustic a) Response to prescribed acoustic source b) Acoustic impedance boundary operator and radiation impedance operator c) Helmholtz integral representations d) Boundary integral equations e) Finite elements discretization 2) External vibroacoustic 3) Internal vibroacoustic

Definition of scales in heterogeneous solids; notion of Representative Volume Element(RVE); Kinematically or Statically Uniform Boundary Conditions; RVE stiffness or compliance tensor; Eshelby problem and Green operators. Voigt and Reuss bounds, Hashin-Shtrikman bounds, dilute, Mori-Tanaka and autocoherent models. Homogenization of periodic media, asymptotic methods, Lippmann-Schwinger equation, resolution with iterative méthods based on fast Fourier Transform (FFT)

Introduction; probabilistic models for vector-valued random variables​​; construction of probability laws; stochastic fields; methods for solving equations with random parameters; nonparametric probabilistic models for uncertainties in dynamics.

English for oral presentation in international scientific events; English for writing scientific articles.

Complex fluids vs Newtonian fluids : Modelling and identification of highly viscous behaviors; nonlinear viscosity and Bighman fluids. Hele Shaw approximation and numerical modelling of viscous flows. Thermal aspects (WLF law, self-heating, exchange with tools); numerical simulation of thermo-mechanical coupled problem. Visco-elastic behavior in finite strain.

Plane waves in isotropic fluids and solids. Acoustic impedance at normal incidence in fluids, and highly porous materials. Acoustic impedance at oblique incidence in fluids, and highly porous materials. Examples : reflection coefficient and absorption coefficient at normal and oblique incidence for multi-layered materials (Matlab and dedicated software).

Perfect thermal interfaces. Hadamard relation for temperature jump. Continuity and discontinuity conditions for temperature/heat flux gradients. Fourier's law for perfect interfaces; Perfect elastic interface. Hadamard compatibility condition for displacements. Continuity/discontinuity conditions for displacements and stresses. Hooke's law for perfect interfaces; Perfect multi physical interface. Hadamard compatibility equation. Generalized Hill interface operators. Solution for perfect interfaces in a composite (multi-physical framework). Homogenization of laminates ; Asymptotic analysis for imperfect interfaces in a multi-physical context. General forms for displacement vectors and generalized constraints jumps. Special cases (Kapitza law, Gurtin-Murdoch relation, ...); Application of imperfect interface models in micromechanics and nanomechanics.

Computation of effective properties for linear diffusion/elasticity problems; numerical homogenization of coupled problems: thermoelasticity, poroelasticity and electromechanical coupling; Introduction to advanced techniques for the homogenization of nonlinear heterogeneous structures

Basics in probability theory, utility function and limit states, structural reliability, numerical simulations, simplified methods and reliability index, applications.

Introduction to topological optimization by homogenization. 1) Reminder of variational principles;2) Formulation of the problem of minimization of compliance and non-existence of a solution to the problem {0.1} ;3) Elements of homogenization and introduction to composite theory; 4) Formulation of the relaxed problem and numerical implementation; 5) Anisotropic elastic materials

Le stage doit permettre à l’étudiant de mettre en application l’ensemble des connaissances acquises durant sa formation académique et d'acquérir des compétences additionnelles en matière d’initiation à la recherche (dans le contexte d’un laboratoire ou dans un secteur R&D d’une entreprise).