A robust and efficient rate-independent crystal plasticity model based on successive one-dimensional solution steps

Abstract

An efficient stress update algorithm for rate-independent crystal plasticity is presented. A series of successive one-dimensional solution (SODS) steps traces the hypersurfaces describing the slip state for which the yield criteria of individual slip systems are fulfilled to identify the intersection of all hypersurfaces. This provides both the active set and all slip components without requiring iterative active set search procedures or inducing spurious slip on inactive systems. The basic SODS algorithm is accelerated by tracking the evolution of the active set. A fast Newton–Raphson procedure enables to obtain the solution for an unchanging active set directly, while line search and extrapolation procedures direct the SODS steps towards the solution faster. A regularised tangent modulus is proposed that eliminates stiffness jumps upon changes in active set to improve the convergence behaviour of outer (equilibrium) iterations conducted with the algorithm. The resulting stress update algorithm is highly stable and efficient, making it an attractive candidate for use in large-scale crystal plasticity FE simulations and homogenisation algorithms.