A phase-field approach to pneumatic fracture

Phase-field methods for brittle fracture employ a variational framework and have proven to predict complex fracture patterns in two and three dimensional examples. This contribution focuses on a phase-field approach for a coupled field model of brittle pneumatic fracture. Two different challenges are tackled in this contribution: First, we have to deal with pressure-driven processes within the proposed phase-field ansatz, second, we have to consider the numerical effort of the simulations. Our phase-field formulation is based on elasticity and a suitable operator split to take only the tensile parts into account. Furthermore, a prescribed pressure is coupled with the phase-field parameter to consider crack propagation induced by pneumatic pressure. To keep the numerical effort as small as possible we apply a specifically developed multigrid method for three-dimensional problems. The accuracy and the robustness of the solution method will be demonstrated with a series of numerical examples.