Discontinuous and Enriched Galerkin Methods for Phase-Field Fracture Propagation in Elasticity.

In this work, we introduce discontinuous Galerkin and enriched Galerkin formulations for the spatial discretization of phase-field fracture propagation. The nonlinear coupled system is formulated in terms of the Euler-Lagrange equations, which are subject to a crack irreversibility condition. The resulting variational inequality is solved in a quasi-monolithic way in which the irreversibility condition is incorporated with the help of an augmented Lagrangian technique. The relaxed nonlinear system is treated with Newton's method. Numerical results complete the present study.