Computational Homogenization of Heterogeneous Materials with Finite Elements

Description

This monograph provides a concise overview of the main theoretical and numerical tools to solve homogenization problems in solids with finite elements. Starting from simple cases (linear thermal case) the problems are progressively complexified to finish with nonlinear problems. The book is not an overview of current research in that field, but a course book, and summarizes established knowledge in this area such that students or researchers who would like to start working on this subject will acquire the basics without any preliminary knowledge about homogenization. More specifically, the book is written with the objective of practical implementation of the methodologies in simple programs such as Matlab. The presentation is kept at a level where no deep mathematics are required.​ Front Matter ....Pages i-xvi Introduction (Julien Yvonnet)....Pages 1-6 Review of Classical FEM Formulations and Discretizations (Julien Yvonnet)....Pages 7-27 Conduction Properties (Julien Yvonnet)....Pages 29-51 Elasticity and Thermoelasticity (Julien Yvonnet)....Pages 53-89 Piezoelectricity (Julien Yvonnet)....Pages 91-102 Saturated Porous Media (Julien Yvonnet)....Pages 103-121 Linear Viscoelastic Materials (Julien Yvonnet)....Pages 123-144 When Scales Cannot Be Separated: Direct Solving of Heterogeneous Structures with an Advanced Multiscale Method (Julien Yvonnet)....Pages 145-160 Nonlinear Computational Homogenization (Julien Yvonnet)....Pages 161-209 Back Matter ....Pages 211-221