A DG/CR discretization for the variational phase-field approach to fracture

Variational phase-field models of fracture are widely used to simulate nucleation and propagation cracks in brittle materials. They based on the approximation solutions a free-discontinuity energy by two smooth function: displacement damage field. Their numerical implementation is typically discretization both fields nodal $$\mathbb {P}^1$$ Lagrange finite elements. In this article, we propose nonconforming discontinuous elements for elements, whose gradient more isotropic, damage. The handling nonconformity derived from that heterogeneous diffusion problems. We illustrate robustness versatility proposed method through series examples.