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

In this work, different composite voxel methods are proposed to deal with inelastic materials with multiple 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 polycrystalline aggregate. According to the results, the Voigt approximation, which ignores morphological features, 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 experimental 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.