Journal
NONLINEARITY
Volume 28, Issue 5, Pages 1371-1399Publisher
IOP Publishing Ltd
DOI: 10.1088/0951-7715/28/5/1371
Keywords
pressurized fractures; phase field; quasi-static model; incremental formulation; Biot's consolidation equations
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Funding
- US Department of Energy, Office of Science, Office of Basic Energy Sciences through DOE [DE-FG02-04ER25617, MOD. 010]
- Conoco Phillips
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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.
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