On the numerical implementation of non-smooth domains. Part I: Rate-dependent formulations

Abstract
This work addresses the formulation and numerical implementation of classical crystal plasticity formulations, which are characterised by non-smooth elastic domains or yield/potential surfaces. The predictive capabilities of existing rate-dependent crystal plasticity models and algorithms when subjected to complex multiaxial loading paths are investigated in the quasi-rateindependent regime. In order to compare consistently the performance of the different models, a generic thermodynamics-based crystal plasticity framework, which incorporates current formulations as special cases, is formulated. Several two-dimensional boundary values problems for elasto-visco plastic FCC crystals are selected as benchmark cases. Particular emphasis is placed on investigating the effects of multi-axial loading paths and latent hardening on the selection of active slip systems at sharp yield surface corners. The results clearly show that the implementation method strongly influences the predicted multi-axial stress paths due to differences in the types of slip systems which are successively activated as deformation progresses.