Details
| Original language | English |
|---|---|
| Article number | 1371 |
| Pages (from-to) | 1371-1399 |
| Number of pages | 29 |
| Journal | NONLINEARITY |
| Volume | 28 |
| Issue number | 5 |
| Publication status | Published - 1 May 2015 |
| Externally published | Yes |
Abstract
In this paper we present a quasi-static formulation of a phase-field model for a pressurized crack in a poroelastic medium. The mathematical model represents a linear elasticity system with a fading Gassman tensor as the crack grows, that is coupled with a variational inequality for the phase-field variable containing an entropy inequality. We introduce a novel incremental approximation that decouples displacement and phase-field problems. We establish convergence to a solution of the quasi-static problem, including Rice's condition, when the time discretization step goes to zero. Numerical experiments confirm the robustness and efficiency of this approach for multidimensional test cases.
Keywords
- Biot's consolidation equations, Incremental formulation, Phase field, Pressurized fractures, Quasi-static model
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Mathematics(all)
- Mathematical Physics
- Physics and Astronomy(all)
- Mathematics(all)
- Applied Mathematics
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In: NONLINEARITY, Vol. 28, No. 5, 1371, 01.05.2015, p. 1371-1399.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A quasi-static phase-field approach to pressurized fractures
AU - Mikelić, Andro
AU - Wheeler, Mary F.
AU - Wick, Thomas
N1 - Publisher Copyright: © 2015 IOP Publishing Ltd & London Mathematical Society. Copyright: Copyright 2015 Elsevier B.V., All rights reserved.
PY - 2015/5/1
Y1 - 2015/5/1
N2 - In this paper we present a quasi-static formulation of a phase-field model for a pressurized crack in a poroelastic medium. The mathematical model represents a linear elasticity system with a fading Gassman tensor as the crack grows, that is coupled with a variational inequality for the phase-field variable containing an entropy inequality. We introduce a novel incremental approximation that decouples displacement and phase-field problems. We establish convergence to a solution of the quasi-static problem, including Rice's condition, when the time discretization step goes to zero. Numerical experiments confirm the robustness and efficiency of this approach for multidimensional test cases.
AB - In this paper we present a quasi-static formulation of a phase-field model for a pressurized crack in a poroelastic medium. The mathematical model represents a linear elasticity system with a fading Gassman tensor as the crack grows, that is coupled with a variational inequality for the phase-field variable containing an entropy inequality. We introduce a novel incremental approximation that decouples displacement and phase-field problems. We establish convergence to a solution of the quasi-static problem, including Rice's condition, when the time discretization step goes to zero. Numerical experiments confirm the robustness and efficiency of this approach for multidimensional test cases.
KW - Biot's consolidation equations
KW - Incremental formulation
KW - Phase field
KW - Pressurized fractures
KW - Quasi-static model
UR - http://www.scopus.com/inward/record.url?scp=84927626211&partnerID=8YFLogxK
U2 - 10.1088/0951-7715/28/5/1371
DO - 10.1088/0951-7715/28/5/1371
M3 - Article
AN - SCOPUS:84927626211
VL - 28
SP - 1371
EP - 1399
JO - NONLINEARITY
JF - NONLINEARITY
SN - 0951-7715
IS - 5
M1 - 1371
ER -