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  • © 2019

Computational Homogenization of Heterogeneous Materials with Finite Elements

Authors:

  • 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

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

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xvi
  2. Introduction

    • Julien Yvonnet
    Pages 1-6
  3. Conduction Properties

    • Julien Yvonnet
    Pages 29-51
  4. Elasticity and Thermoelasticity

    • Julien Yvonnet
    Pages 53-89
  5. Piezoelectricity

    • Julien Yvonnet
    Pages 91-102
  6. Saturated Porous Media

    • Julien Yvonnet
    Pages 103-121
  7. Linear Viscoelastic Materials

    • Julien Yvonnet
    Pages 123-144
  8. Nonlinear Computational Homogenization

    • 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.​

Authors and Affiliations

  • MSME Laboratory, Université Paris-Est Marne-la-Vallée, Marne-la-Vallée Cedex 2, France

    Julien Yvonnet

Bibliographic Information

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 159.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access