A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium

This work considers a Stokes flow in a deformable fracture interacting with a linear elastic medium. To this end, we employ a phase-field model to approximate the crack dynamics. Phase-field methods belong to interface-capturing approaches in which the interface is only given by a smeared zone. For multi-domain problems, the accuracy of the coupling conditions is, however, of utmost importance. Here, interface-tracking methods are preferred, since the interface is resolved on mesh edges up to discretisation errors, but it does not depend on the length scale parameter of some smeared zone. The key objective of this work is to construct a robust framework that computes first a crack path via the phase-field method (interface-capturing) and then does an interface-tracking reconstruction. We then discuss several approaches to reconstruct the Eulerian description of the open crack domain. This includes unfitted approaches where a level-set of the crack interface is constructed and an approach where the geometry is re-meshed. Using this reconstructed domain, we can compute the fluid-structure interaction problem between the fluid in the crack and the interacting solid. With the explicit mesh reconstruction of the two domains, we can then use an interface-tracking Arbitrary-Lagrangian-Eulerian (ALE) discretisation approach for the resulting fluid-structure interaction (FSI) problem. Our algorithmic procedure is realised in one final numerical algorithm and one implementation. We substantiate our approach using several numerical examples based on Sneddon's benchmark and corresponding extensions to Stokes fluid-filled regimes.

Automated summary

This work studied the interaction between a Stokes flow in a deformable fracture and a linear elastic medium. The crack dynamics were approximated using a phase-field model, which captures the interface by a smeared zone. The main objective was to construct a robust framework that first computes the crack path using the phase-field method and then does an interface-tracking reconstruction. Various approaches for reconstructing the open crack domain were discussed, including unfitted approaches and remeshing. Numerical examples based on Sneddon's benchmark were used to substantiate the approach.