An affine formulation of eigenstrain-based homogenization method and its application to polycrystal plasticity

Abstract

Abstract Reduced order models (ROMs) are typically incorporated into concurrent multiscale approaches to allow for efficient nonlinear multiscale simulations and to alleviate high cost of direct nonlinear computational homogenization schemes. ROMs based on the ideas of transformation field analysis are among the most popular in the literature since they only require linear elastic simulations for model construction and typically have low number of degrees of freedom. However, these models have been shown to deliver overly stiff response in simulating wide range of materials. The present study focuses on mitigating this problem in the context of eigenstrain-based homogenization method (EHM) using instantaneous moduli information for polycrystal elastoviscoplasticity. For this purpose, a new EHM model is developed with the intention of using affine moduli for recomputation of the instantaneous localization tensors. The accuracy of the method is compared to the original EHM and direct crystal plasticity finite element simulations for several synthetic polycrystal microstructures, loading conditions and varying phase contrast. We show that the affine model delivers consistently softer response compared to the original EHM model. In particular, the affine model delivers notably more accurate response in the presence of high phase contrast. The affine EHM is able to capture local load redistribution through recomputation of the localization tensors.