pfm-cracks: A parallel-adaptive framework for phase-field fracture propagation

This paper describes the main features of our parallel-adaptive open-source framework for solving phase-field fracture problems called pfm-cracks. Our program allows for dimension-independent programming in two- and three-dimensional settings. A quasi-monolithic formulation for the coupled two-component system of displacements and a phase-field indicator variable is used. The nonlinear problem is solved with a robust, efficient semi-smooth Newton algorithm. A highlight is adaptive predictor–corrector mesh refinement. The code is fully parallelized and scales to 1000 and more MPI ranks. Illustrative tests demonstrate the current capabilities, from which some are parts of benchmark collections

Schur‐type preconditioning of a phase‐field fracture model in mixed form

In the context of phase-field modeling of fractures in incompressible materials, a mixed form of the elasticity equation can overcome possible volume locking effects. The drawback is that a coupled variational inequality system with three unknowns (displacements, pressure and phase-field) has to be solved, which increases the overall workload. Efficient preconditioning at this point is an indispensable tool. In this work, a problem-specific iterative solver is proposed leveraging the saddle-point structure of the displacement and pressure variable. A Schur-type preconditioner is developed to avoid ill-conditioning of the phase-field fracture problem. Finally, we show numerical results of a pressure-driven benchmark which to confirm the robustness of the solver