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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 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. [ABSTRACT FROM AUTHOR]

The macroscopic behavior of polycrystalline materials is largely influenced by the shape, the arrangement and the orientation of crystallites. Different methods have thus been developed to determine the effective behavior of such materials as a function of their microstructural features. In this work, which focuses on polycrystalline materials with an elastic–viscoplastic behavior, the self-consistent, finite element and spectral methods are compared. These common methods are used to determine the effective behavior of different 316L polycrystalline aggregates subjected to various loading conditions. Though no major difference is observed at the macroscopic scale, the hardening rate is found to be slightly overestimated with the finite element method. Indeed, spatial convergence cannot be guaranteed for finite element calculations, even when fine mesh resolutions, for which the computational cost is important, are used. Also, as the self-consistent method does not explicitly account for neighborhood effects, important discrepancies between the self-consistent method and the other methods exist regarding the mechanical response of a specific grain. The self-consistent method nevertheless provides a reasonable description of the average response obtained for a group of grains with identical features (e.g. shape, orientation). [ABSTRACT FROM AUTHOR]