Adaptive refinement for phase-field models of brittle fracture based on Nitsche's method

“This is a post-peer-review, pre-copyedit version of an article published in Computational mechanics. The final authenticated version is available online at: http://dx.doi.org/10.1007/s00466-020-01841-1”. A new adaptive refinement strategy for phase-field models of brittle fracture is proposed. The approach provides a computationally efficient solution to the high demand in spatial resolution of phase-field models. The strategy is based on considering two types of elements: h-refined elements along cracks, where more accuracy is needed to capture the solution, and standard elements in the rest of the domain. Continuity between adjacent elements of different type is imposed in weak form by means of Nitsche's method. The weakly imposition of continuity leads to a very local refinement in a simple way, for any degree of approximation and both in 2D and 3D. The performance of the strategy is assessed for several scenarios in the quasi-static regime, including coalescence and branching of cracks in 2D and a twisting crack in 3D.