Consistent crystal plasticity kinematics and linearization for the implicit finite element method

Purpose - The purpose of this paper is to describe several novel techniques for implementing a crystal plasticity (CP) material model in a large deformation, implicit finite element framework. Design/methodology/approach - Starting from the key kinematic assumptions of CP, the presentation develops the necessary CP correction terms to several common objective stress rates and the consistent linearization of the stress update algorithm. Connections to models for slip system hardening are isolated from these processes. Findings - A kinematically consistent implementation is found to require a correction to the stress update to include plastic vorticity developed by slip deformation in polycrystals. A simpler, more direct form for the algorithmic tangent is described. Several numerical examples demonstrate the capabilities and computational efficiency of the formulation. Research limitations/implications - The implementation assumes isotropic slip system hardening. With simple modifications, the described approach extends readily to anisotropic coupled or uncoupled hardening functions. Practical implications - The modular formulation and implementation support streamlined development of new models for slip system hardening without modifications of the stress update and algorithmic tangent computations. This implementation is available in the open-source code WARP3D. Originality/value - In the process of developing the CP formulation, this work realized the need for corrections to the Green-Naghdi and Jaumann objective stress rates to account properly for non-zero plastic vorticity. The paper describes fully the consistent linearization of the stress update algorithm and details a new scheme to implement the model with improved efficiency.