Different composite voxel methods for the numerical homogenization of heterogeneous inelastic materials with FFT-based techniques

Abstract

FFT-based homogenization methods aim at calculating the effective behavior of heterogeneous materials with periodic microstructures. These methods operate on a regular grid of voxels, and hence require an appropriate spatial discretization of periodic microstructures. However, when different microstructural length scales are involved, it is not always possible to have sufficient spatial resolutions to explicitly consider the influence of fine microstructural features (e.g. voids, second-phase particles). To circumvent this difficulty, one solution consists of using composite voxel methods to define the effective properties and the effective internal variables of heterogeneous voxels. In this work, different composite voxel methods are proposed to deal with inelastic materials with mul- tiple length scales. These methods use simple homogenization rules to calculate the effective behavior of heterogeneous voxels. The first part of this paper is dedicated to the description of the composite voxel methods, which are based either on the Voigt, laminate structure or Mori–Tanaka approximations. In the second part, these methods are used to model the elasto-plastic behavior of a pearlitic steel poly- crystalline aggregate. According to the results, the Voigt approximation, which ignores morphological fea- tures, is not appropriate for treating heterogeneous voxels. When morphological information is accounted for, with either the laminate structure or Mori–Tanaka approximations, a better agreement with experi- mental observations is obtained. Though none of these methods is universal, they offer some possibilities to investigate the mechanical behavior of heterogeneous materials involving multiple length scales.