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

Abstract

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.