Speaker
Description
We consider the coupled, multi-domain, multi-physics problem posed by a fluid-filled, pressurised fracture in an intact solid medium surrounding the fluid. For example, such a setting may be found in Enhanced Geothermal Systems or nuclear waste management.
A well-established method for dealing with cracks is the phase-field fracture (PFF) approach. This method is effective as it can deal with propagating fractures, splitting fractures and topology changes. This approach captures the fracture interface by approximating the fracture by a diffusive zone. While this gives the method its favourable properties, the smeared interface causes complications when complex physics at the boundary between the fluid-filled crack and the surrounding medium are needed.
We consider a geometry reconstruction approach to capture the effects at the interface. Based on the crack opening displacements (or fracture width), we obtain a description of the interface between the solid and the fluid-filled crack. With this geometry at hand, we can pose a stationary thermo-fluid-structure interaction problem, which incorporates the physics at the interface. In particular, we can use interface tracking methods, such as arbitrary Lagrangian-Eulerian finite element methods, to solve the fluid-structure interaction (FSI) problem in this domain.
The challenge now lies in coupling results from the FSI problem back to the PFF. The temperature and pressure drive the fracture problem. However, the FSI temperature and pressure exist on a different geometry than the PFF problem. Furthermore, the FSI pressure only exists inside the fracture, while the PFF model assumes the ex- istence of a global pressure. To deal with this problem, we propose two approaches. The first is based on an averaged pressure, which may be evaluated globally. The second approach derives a novel phase-field fracture model, incorporating the driving force contributions through appropriate boundary integrals. Consequently, the open crack geometry can also be utilised for the PFF problem. We present several numerical examples illustrating the potential of both approaches.
