Accepted for publication in Journal of Computational Physics, 2016, doi: 10.1016/j.jcp.2016.09.024 Coupling fluid-structure interaction with phase-field fracture Thomas Wick * In this work, a concept for coupling fluid-structure interaction with brittle fracture in elasticity is proposed. The fluid-structure interaction problem is modeled in terms of the arbitrary Lagrangian-Eulerian technique and couples the isothermal, incompressible Navier-Stokes equations with nonlinear elastodynamics using the Saint-Venant Kirchhoff solid model. The brittle fracture model is based on a phase-field approach for cracks in elasticity and pressurized elastic solids. In order to derive a common framework, the phase- field approach is re-formulated in Lagrangian coordinates to combine it with fluid-structure interaction. A crack irreversibility condition, that is mathematically characterized as an inequality constraint in time, is enforced with the help of an augmented Lagrangian it- eration. The resulting problem is highly nonlinear and solved with a modified Newton method (e.g., error-oriented) that specifically allows for a temporary increase of the resid- uals. The proposed framework is substantiated with several numerical tests. In these examples, computational stability in space and time is shown for several goal functionals, which demonstrates reliability of numerical modeling and algorithmic techniques. But also current limitations such as the necessity of using solid damping are addressed. Keywords: fluid-structure interaction, arbitrary Lagrangian-Eulerian technique, pressurized phase- field fracture, dynamic brittle fracture, augmented Lagrangian approach, finite elements 1 Introduction Both fluid-structure interaction (FSI) and fracture propagation are current but challenging topics with numerous applications in applied mathematics and engineering. For FSI literature we exemplary refer to the books [8, 16, 17, 33, 36] and for fracture mechanics we refer to [4, 12, 42, 67, 70, 71, 82]; and references cited therein are also emphasized. The goal of this work is to bring both frameworks together. This is of great interest since often FSI settings should also be able to account for fracture (or damage) of the solid part. On the other hand, single or multiple fractures or fracture networks can be found, for instance, in geomechanics, geophysics and porous media, which are possibly filled with fluids or coupled to surrounding flow. Thus, a framework that contains elastodynamics (which do also allow to account for large solid deformations), fluid flow, and a model for fracture representation and propagation is of current interest. * Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences, Al- tenberger Str. 69, 4040 Linz, Austria 1
Coupling fluid-structure interaction with phase-field fracture
Jul 01, 2023
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