Adaptive and Pressure-Robust Discretization of Incompressible Pressure-Driven Phase-Field Fracture

In this work, we consider pressurized phase-field fracture problems in nearly and fully incompressible materials. To this end, a mixed form for the solid equations is proposed. To enhance the accuracy of the spatial discretization, a residual-type error estimator is developed. Our algorithmic advancements are substantiated with several numerical tests that are inspired from benchmark configurations. Therein, a primal-based formulation is compared to our newly developed mixed phase-field fracture method for Poisson ratios approaching $\nu \to 0.5$. Finally, for $\nu = 0.5$, we compare the numerical results of the mixed formulation with a pressure robust modification.