LAUSR

This article presents a dissipation‐based path‐following technique for the phase‐field approach to brittle and ductile fracture. This technique allows computing the post‐peak response of solids loaded by external forces and snap‐backs in the softening stage. By controlling the dissipated energy during loading, the solid is prevented from unloading elastically, and an equilibrium branch with a continuous increase of dissipated energy is followed. Because solids can dissipate in both tension and compression, a discontinuous equilibrium path can be obtained. To avoid this occurrence, two novel techniques are presented, which ensure a continuous equilibrium path for which the solid is either in tension or compression. In addition, the thermodynamic constraints present in the phase‐field model are rigorously solved using an interior‐point method. In order to allow for simultaneous dissipation due to both plastic and damage mechanisms, the governing equations are solved monolithically. The presented method is tested on four benchmark problems, and it is observed that by tracing snap‐backs, time‐discontinuous evolutions are avoided, which restores energy balance and enhances the convergence of the monolithic scheme.