On polarization-based schemes for the FFT-based computational homogenization of inelastic materials

We revisit the polarization-based schemes introduced to FFT-based computational homogenization by Eyre-Milton, Michel-Moulinec-Suquet and Monchiet-Bonnet. When applied to nonlinear problems, these polarization-based methods suffer from two handicaps. Firstly, the optimal choice of algorithmic parameters is only known for the linear elastic case. Secondly, in its original version each iteration of the polarization scheme requires solving a nonlinear system of equations for each voxel. We overcome both difficulties for small-strain elastic-viscoplastic materials. In particular, we show how to avoid solving the nonlinear system. As a byproduct, we identify a computationally efficient convergence criterion enabling a fair comparison to gradient-based solvers (like the basic scheme). The convergence behavior of the polarization schemes is compared to the basic scheme of Moulinec-Suquet and fast gradient methods, based on numerical demonstrations.