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. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)