A combined finite element–finite volume framework for phase-field fracture

Numerical simulations of brittle fracture using phase-field approaches often employ a discrete approximation framework that applies the same order interpolation for displacement and variables. In particular, use linear finite elements to discretize both stress equilibrium equations is widespread in literature. However, P1 Lagrange shape functions model not optimal, as latter contains cusps fully developed cracks. These should turn occur at locations corresponding Gauss points associated FE mechanics. Such feature challenging reproduce accurately with low elements, element sizes must consequently be made very small relative regularization parameter achieve convergence results respect mesh. this paper, we combine standard discretization cell-centered volume evolution equation based on two-point flux constructed over simplex Compared pure formulation utilizing proposed looser restrictions mesh refinement length scale. This ability coarser meshes traditional implementation allows significant reductions computational cost, demonstrated several numerical examples.