An introduction to periodic homogenization/ Alain Damlamian -- The periodic unfolding method in homogenization/ Alain Damlamian -- Deterministic homogenization of stationary Navier-Stokes type equations / Gabriel Nguetseng and Lazarus Signing -- Homogenization of a class of imperfect transmission problems / Patricia Donato -- Decompositions of displacements of thin structures / Georges Griso -- Decomposition of rods deformations. Asymptotic behavior of nonlinear elastic rods / Georges Griso -- Junction of a periodic family of rods with a plate in elasticity / Dominique Blanchard -- Multi-scale modelling of new composites: theory and numerical simulation / Bernadette Miara -- A priori and a posteriori error analysis for numerical homogenization: a unified framework / Assyr Abdulle
Summary
The focus of this is on the latest developments related to the analysis of problems in which several scales are presented. After a theoretical presentation of the theory of homogenization in the periodic case, the other contributions address a wide range of applications in the fields of elasticity (asymptotic behavior of nonlinear elastic thin structures, modeling of junction of a periodic family of rods with a plate) and fluid mechanics (stationary Navier-Stokes equations in porous media). Other applications concern the modeling of new composites (electromagnetic and piezoelectric materials) and imperfect transmission problems. A detailed approach of numerical finite element methods is also investigated
