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

Henry von Wahl, Thomas Wick

TL;DR

This paper introduces a fully coupled framework that combines a high-accuracy phase-field fracture model with an ALE-based fluid-structure interaction solver for a Stokes flow inside a fluid-filled crack surrounded by an elastic medium. The key advance is to switch from interface-capturing to interface-tracking via mesh reconstruction, enabling sharp interface conditions to be imposed on the crack boundary and a reconstructed open crack domain for the FSI problem. The authors formulate a pressurized phase-field fracture problem with explicit interface terms, solve it iteratively with an open-crack domain reconstruction, and couple to a Stokes FSI problem with averaged crack pressure feeding back into the phase-field model. Numerical tests on Sneddon-type configurations and propagating cracks demonstrate accurate COD/TCV convergence and qualitatively correct fracture evolution under stationary and quasi-static loading; the work provides a path toward fully time-dependent, multi-physics fracture simulations. The approach has potential applications in subsurface and biomedical contexts where accurate interface conditions and evolving fracture geometry are critical.

Abstract

In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid-structure interaction. The key motivation is to utilize 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 realized 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.

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

TL;DR

This paper introduces a fully coupled framework that combines a high-accuracy phase-field fracture model with an ALE-based fluid-structure interaction solver for a Stokes flow inside a fluid-filled crack surrounded by an elastic medium. The key advance is to switch from interface-capturing to interface-tracking via mesh reconstruction, enabling sharp interface conditions to be imposed on the crack boundary and a reconstructed open crack domain for the FSI problem. The authors formulate a pressurized phase-field fracture problem with explicit interface terms, solve it iteratively with an open-crack domain reconstruction, and couple to a Stokes FSI problem with averaged crack pressure feeding back into the phase-field model. Numerical tests on Sneddon-type configurations and propagating cracks demonstrate accurate COD/TCV convergence and qualitatively correct fracture evolution under stationary and quasi-static loading; the work provides a path toward fully time-dependent, multi-physics fracture simulations. The approach has potential applications in subsurface and biomedical contexts where accurate interface conditions and evolving fracture geometry are critical.

Abstract

In this work, we couple a high-accuracy phase-field fracture reconstruction approach iteratively to fluid-structure interaction. The key motivation is to utilize 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 realized 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.
Paper Structure (50 sections, 48 equations, 16 figures, 2 algorithms)

This paper contains 50 sections, 48 equations, 16 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. A phase-field fluid-structure interaction framework
  3. Notation
  4. Phase-Field Fracture
  5. Stationary Fluid-Structure Interaction
  6. Interface reconstruction, and coupled algorithm, and discretisation
  7. Interface reconstruction
  8. Pressure coupling
  9. Final algorithm
  10. Spatial discretization
  11. Numerical solution
  12. Numerical tests
  13. Example 1: Sneddon test with Formulation \ref{['form_2_interface_b']}
  14. Configuration
  15. Results
  16. ...and 35 more sections

Figures (16)

  • Figure 1: Crack opening displacement convergence for Sneddon's test computed computed using \ref{['form_2_interface_b']}.
  • Figure 2: Example 2: Fluid-filled phase-field crack coupled with the fluid-structure-interaction pressure. Left: Resulting crack shape based on the crack opening displacements after four sub-iterations between the phase-field and the fluid-structure-interaction problem with $lvl\in\{4, 5\}$ levels of mesh refinement. Right: Fluid-Structure interaction pressure on the reconstructed domain used to drive the divergence from Sneddon's test on mesh level three.
  • Figure 3: Example 2: Fluid-filled phase-field crack coupled with the fluid-structure-interaction pressure. Left: Numerical convergence for the crack opening displacements in two points. Right: Numerical convergence of the total crack volume.
  • Figure 4: Example 3: Phase-field-deformation (vertical component) and phase-field after three levels of mesh refinement.
  • Figure 5: Example 3: FSI-deformation magnitude, velocity magnitude and FSI-pressure after three levels of mesh refinement.
  • ...and 11 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2