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.