An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework

Abstract

Computational homogenization schemes based on the fast Fourier transform (FFT) enable studying the effective micromechanical behavior of polycrystalline microstructures with complex morphology. In the conventional strain-based setting, evaluating the single crystal elasto-viscoplastic constitutive law involves solving a non-linear system of equations which dominates overall runtime. Evaluating the inverse material law is much less costly in the small-strain context, because the flow rule is an explicit function of the stress.We revisit the primal and dual formulation of the unit cell problem of computational homogenization and use state of the art FFT-based algorithms for its solution. Performance and convergence behavior of the different solvers are investigated for a polycrystal and a fibrous microstructure of a directionally solidified eutectic.