Details
| Original language | English |
|---|---|
| Pages (from-to) | 67-96 |
| Number of pages | 30 |
| Journal | Journal of computational physics |
| Volume | 327 |
| Publication status | Published - 1 Dec 2016 |
| Externally published | Yes |
Abstract
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 iteration. 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 residuals. 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
- Arbitrary Lagrangian–Eulerian technique, Augmented Lagrangian approach, Dynamic brittle fracture, Finite elements, Fluid–structure interaction, Pressurized phase-field fracture
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
- Physics and Astronomy(all)
- Physics and Astronomy (miscellaneous)
- Physics and Astronomy(all)
- General Physics and Astronomy
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Journal of computational physics, Vol. 327, 01.12.2016, p. 67-96.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Coupling fluid–structure interaction with phase-field fracture
AU - Wick, Thomas
N1 - Publisher Copyright: © 2016 Elsevier Inc. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - 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 iteration. 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 residuals. 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.
AB - 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 iteration. 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 residuals. 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.
KW - Arbitrary Lagrangian–Eulerian technique
KW - Augmented Lagrangian approach
KW - Dynamic brittle fracture
KW - Finite elements
KW - Fluid–structure interaction
KW - Pressurized phase-field fracture
UR - http://www.scopus.com/inward/record.url?scp=84988884421&partnerID=8YFLogxK
U2 - 10.1016/j.jcp.2016.09.024
DO - 10.1016/j.jcp.2016.09.024
M3 - Article
AN - SCOPUS:84988884421
VL - 327
SP - 67
EP - 96
JO - Journal of computational physics
JF - Journal of computational physics
SN - 0021-9991
ER -