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Article Dans Une Revue Nonlinearity Année : 2015

A quasistatic phase field approach to pressurized fractures

Résumé

In this paper we present a quasistatic 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 quasistatic 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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Dates et versions

hal-01138344 , version 1 (28-04-2015)
hal-01138344 , version 2 (02-03-2016)

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Andro Mikelic, M.F. Wheeler, Thomas Wick. A quasistatic phase field approach to pressurized fractures. Nonlinearity, 2015, 28 (5), pp.1371-1399. ⟨10.1088/0951-7715/28/5/1371⟩. ⟨hal-01138344v2⟩
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