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

TL;DR

This paper presents a robust framework combining phase-field and interface-tracking methods to accurately reconstruct crack interfaces in fluid-filled fractures within elastic media, improving fluid-structure interaction simulations.

Contribution

It introduces a novel combined approach for phase-field crack modeling and explicit interface reconstruction, enhancing accuracy in fluid-structure interaction problems.

Findings

Accurate crack path reconstruction using phase-field and interface-tracking methods.

Effective fluid-structure interaction simulation in Stokes flow within fractures.

Validation on benchmark problems demonstrating improved accuracy.

Abstract

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 discretization 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.