A rate-independent crystal plasticity algorithm based on the interior point method

Abstract

A robust rate-independent crystal plasticity algorithm is proposed where the amount of plastic slip required to satisfy the multi-surface yield conditions are determined using a flow rule that stems from the maximization of plastic dissipation. The stress update procedure, which is based on the backward Euler time integration, is treated as an optimization problem and the interior point method is utilized in obtaining the stress. As opposed to common return mapping algorithms, such as the closest point projection method, the yield conditions are not violated during the iterative update of the slip amounts which helps to avoid convergence issues for both the local consistency and the global equilibrium solutions. An efficient implementation of this method for large deformations is given together with an algorithmic tangent modulus that makes it attractive to be used in both Finite Element simulations as well as analytical homogenization algorithms.