A dissipation-based arc-length method for robust simulation of brittle and ductile failure

A robust method to trace the equilibrium path in non-linear solid mechanics problems is proposed. A general arc-length constraint based on the energy release rate is developed. Constraints have been derived for the cases of geometrically linear damage, geometrically linear plasticity and geometrically non-linear damage. All three constraints can efficiently be applied in a finite element context. Numerical simulations demonstrate that the proposed framework gives robust results for these cases. Applicability of the proposed framework to other types of constitutive and/or kinematic behaviour is predicted. Copyright (C) 2008 John Wiley & Sons, Ltd.