On the numerical implementation of 3D rate-dependent single crystal plasticity formulations

In this paper, several important numerical issues are addressed for three-dimensional (3D) rate-dependent single crystal plasticity. After a thorough comparison of different constitutive algorithms, we classify the integration methods into three approaches, namely, the implicit elastic/plastic deformation gradient approach, the implicit slip-rate approach, and the explicit slip-rate approach. As part of this algorithmic study, we focus on five different schemes to enforce the plastic incompressibility, four ways to update the texture, and one convergence criteria. The numerical performance of these different methods is illustrated. The contribution of this study is three-fold: a stable scheme for the incompressibility enforcement, an improved implicit algorithm, and a fully explicit algorithm.