A new view on the solution of rate-independent crystal plasticity finite element models

The crystal plasticity finite element method (CP-FEM) readily enables microstructure-based material modelling by relating macroscopic plastic deformation to dislocation slip on crystal slip systems. Rate-independent CP models provide physically accurate solutions by allowing slip only if the resolved shear stress on a slip system equals the critical resolved shear stress. However, computing the amount of slip for such models remains challenging. This work proposes a novel stable and efficient stress-update algorithm based on fixed-point iterations. These iterations trace the hypersurfaces that describe the slip state for which individual slip system's yield functions are zero, until all slip system hypersurfaces intersect. This simultaneously provides the set of active slip systems and the slip on these systems, avoiding the need for an iterative active set search algorithm without inducing spurious slip on systems on which the shear stress is below the critical resolved shear stress.