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.
An Introduction to Periodic Homogenization (Alain Damlamian); The Periodic Unfolding Method in Homogenization (Alain Damlamian); Homogenization of Navier - Stokes Equations (Gabriel Nguetseng & 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 Modeling of New Composites, Theory and Numerical Simulation (Bernadette Miara); A Priori and a Posteriori Analysis for Numerical Homogenization: A Unified Framework (Assyr Abdulle).