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

TL;DR

This paper introduces a mixed discretization method for pressure-driven phase-field fracture in incompressible materials, improving accuracy and robustness, especially near the incompressible limit, validated through numerical benchmarks.

Contribution

The paper develops a novel mixed formulation and residual-based error estimator for phase-field fracture in incompressible materials, enhancing accuracy and pressure robustness.

Findings

Mixed formulation outperforms primal-based methods near incompressibility.

Residual error estimator effectively guides adaptive refinement.

Pressure-robust modifications improve results at Poisson ratio 0.5.

Abstract

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.