An Error-Oriented Newton/Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation

The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation. Phase-field fracture consists of two coupled partial differential equations and it is well known that the underlying energy functional is non-convex and sophisticated algorithms are required. For the incremental, spatially-discretized problem, an adaptive error-oriented Newton algorithm is employed, which works as inner loop within an inexact augmented Lagrangian iteration. The latter approach relaxes the crack irreversibility constraint, which is an inequality constraint in time. Several benchmarks are consulted to demonstrate the performance of the algorithmic techniques.