Computational Homogenization of Heterogeneous Materials with Finite Elements

  • Julien Yvonnet

Part of the Solid Mechanics and Its Applications book series (SMIA, volume 258)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Julien Yvonnet
    Pages 1-6
  3. Julien Yvonnet
    Pages 29-51
  4. Julien Yvonnet
    Pages 53-89
  5. Julien Yvonnet
    Pages 91-102
  6. Julien Yvonnet
    Pages 103-121
  7. Julien Yvonnet
    Pages 123-144
  8. Julien Yvonnet
    Pages 161-209
  9. Back Matter
    Pages 211-223

About this book


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.​


Homogenization Virtual materials Multiscale Homogenization simulation Finite Elements Linear phenomena Heterogeneous materials Representative Volume Element strain gradient homogenization periodic boundary conditions in FEM out-of plane properties in 2D problem

Authors and affiliations

  • Julien Yvonnet
    • 1
  1. 1.MSME LaboratoryUniversité Paris-Est Marne-la-ValléeMarne-la-Vallée Cedex 2France

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-030-18382-0
  • Online ISBN 978-3-030-18383-7
  • Series Print ISSN 0925-0042
  • Series Online ISSN 2214-7764
  • Buy this book on publisher's site