Computational Mechanics

, Volume 40, Issue 2, pp 281–298 | Cite as

A numerical method for homogenization in non-linear elasticity

  • I. Temizer
  • T. I. Zohdi
Original Paper


In this work, homogenization of heterogeneous materials in the context of elasticity is addressed, where the effective constitutive behavior of a heterogeneous material is sought. Both linear and non-linear elastic regimes are considered. Central to the homogenization process is the identification of a statistically representative volume element (RVE) for the heterogeneous material. In the linear regime, aspects of this identification is investigated and a numerical scheme is introduced to determine the RVE size. The approach followed in the linear regime is extended to the non-linear regime by introducing stress–strain state characterization parameters. Next, the concept of a material map, where one identifies the constitutive behavior of a material in a discrete sense, is discussed together with its implementation in the finite element method. The homogenization of the non-linearly elastic heterogeneous material is then realized through the computation of its effective material map using a numerically identified RVE. It is shown that the use of material maps for the macroscopic analysis of heterogeneous structures leads to significant reductions in computation time.


Homogenization Elasticity Micromechanics 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringUniversity of CaliforniaBerkeleyUSA

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