Homogenization in linear and non-linear elasticity.

摘要

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 have been investigated where effects of material properties, boundary conditions, test sample size, volume fraction and morphology of heterogeneities were considered. The numerical scheme used to identify the RVE size is then 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.