An energy-based virtual element method framework for polycrystalline plasticity

Abstract

Deformation in an aggregate of single crystalline grains, in conventional crystal plasticity finite element methods, is modeled through the collective behavior of individual ones each consisting of multiple elements. Such a procedure often entails tedious preparedness such as grain-level discretization and post-processing to obtain meaningful collective behavior. Virtual Element Method (VEM) which is designed to take care of a multifaceted three-dimensional body as one element, offers a promising alternative for crystal plasticity modeling. In this paper, we implement a phenomenological, rate-dependent crystal plasticity model within the framework of the energy-based VEM. By integrating nested iterative algorithms with automatic differentiation techniques, the numerical procedure efficiently simulates both single-crystal and polycrystalline solids under various loading conditions. With three numerical examples, we demonstrate the ability of VEM based crystal plasticity modeling to predict stress–strain responses, texture evolutions, and deformation mechanisms in face-centered cubic crystals. This numerical procedure shows a promising method of modeling polycrystalline solids composed of a vast amount of grains, and paves a new route of two-scale modeling which bridges microstructures with macroscopic mechanical behavior of solids.