Computational Homogenization of Heterogeneous Materials with Finite Elements

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.

Presents the theory and methodology starting from simple linear cases up to more complex cases (multiphysics, nonlinear) Includes many points not found in other books, such as the computation of out-of plane properties in 2D problems, practical implementation of periodic boundary conditions in FEM, and handling strain gradient homogenization Provides all details needed to implement the numerical algorithms Provides reference solutions at the end of each chapter so that the user can validate its code Can be used for a course at graduate level

Inhalt
Foreword.- Preface.- Introduction.- Review of classical FEM formulations and discretizations.- Conduction properties.- Elasticity and thermoelasticity.- Piezoelectricity.- Porous media.- Second-order linear homogenization.- Filter-based homogenization.- Nonlinear Computational Homogenization.- Bibliography.- Appendices.- Index.