A coupled high-accuracy phase-field fluid–structure interaction framework for Stokes fluid-filled fracture surrounded by an elastic medium

In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid–structure interaction. The key motivation is to utilise phase-field modelling to compute the fracture path. A mesh reconstruction allows a switch from interface-capturing to interface-tracking in which the coupling conditions can be realised in a highly accurate fashion. Consequently, inside the fracture, a Stokes flow can be modelled that is coupled to the surrounding elastic medium. A fully coupled approach is obtained by iterating between the phase-field and the fluid–structure interaction model. The resulting algorithm is demonstrated for several numerical examples of quasi-static brittle fractures. We consider both stationary and quasi-stationary problems. In the latter, the dynamics arise through an incrementally increasing given pressure.