Thermodynamically consistent phase‐field models of fracture: Variational principles and multi‐field FE implementations

Abstract The computational modeling of failure mechanisms in solids due to fracture based on sharp crack discontinuities suffers in situations with complex crack topologies. This can be overcome by a diffusive crack modeling based on the introduction of a crack phase‐field. In this paper, we outline a thermodynamically consistent framework for phase‐field models of crack propagation in elastic solids, develop incremental variational principles and consider their numerical implementations by multi‐field finite element methods. We start our investigation with an intuitive and descriptive derivation of a regularized crack surface functional that Γ‐converges for vanishing length‐scale parameter to a sharp crack…