A data-based derivation of the internal stress in the discrete-continuum transition regime of dislocation based plasticity

Abstract

Effectively homogenizing microstructure heterogeneity within the coarse-graining volume is a long-lasting challenge in crystal plasticity theories. In this paper, we propose a data-based homogenization method that utilizes discrete dislocation dynamic simulations to derive the nearfield correction stress (back stress) for continuum models. This stress accounts for the effective stress field induced by microstructure heterogeneity under the length scale of a coarse-graining volume, providing a physically based homogenization approach. To bridge the gap between discrete and continuous regimes, we introduce two versions of the nearfield correction stress, as well as a criterion based on microstructure and numerical parameters to determine the discrete and continuous transition. Moreover, by analyzing the mathematical connections with the work-conjugated gradient plasticity theory, we further provide a physical explanation for the observed material length scale in the thermodynamically consistent back stress term. This work presents a novel methodology for effectively addressing microstructure heterogeneity and advancing the understanding and modeling of material behavior bridging different length scales.