TY - JOUR

T1 - A coupled high-accuracy phase-field fluid–structure interaction framework for Stokes fluid-filled fracture surrounded by an elastic medium

AU - von Wahl, Henry

AU - Wick, Thomas

N1 - Funding Information: HvW acknowledges support through the Austrian Science Fund (FWF) project F65. TW thanks Ivan Yotov (University of Pittsburgh) for a fruitful discussion at the \u2018Hot Topics: Recent Progress in Deterministic and Stochastic Fluid\u2013structure Interaction\u2019 Workshop, Dec 2023, in Berkeley, US, during the revision of this paper.

PY - 2024/5

Y1 - 2024/5

N2 - 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.

AB - 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.

KW - Finite elements

KW - Fluid–structure interaction

KW - Interface reconstructions

KW - Phase-field fracture

KW - Sneddon's benchmark

UR - http://www.scopus.com/inward/record.url?scp=85190307740&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2308.15400

DO - 10.48550/arXiv.2308.15400

M3 - Article

AN - SCOPUS:85190307740

VL - 22

JO - Results in Applied Mathematics

JF - Results in Applied Mathematics

M1 - 100455

ER -