Numerical Implementation of Phase-Field Models of Brittle Fracture

These lecture notes address the main challenging computational aspects of phase-field modeling of brittle fracture. We focus, in particular, on the irreversibility constraint and the iterative solution strategy for non-convex minimization problems. In the former case, we present multiple options of incorporating the constraint and discuss the equivalence of the resulting formulations. For the latter, we also consider various available options and critically assess the efficiency and robustness of some of them. Numerical examples on well-known benchmark problems illustrate the theoretical findings.