A quasistatic phase field approach to pressurized fractures

Andro Mikelic (1) , M.F. Wheeler (2) , Thomas Wick (2)

1 ICJ - Institut Camille Jordan
2 ICES - Institute for Computational Engineering and Sciences [Austin]

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 * A.M. would like to thank Institute for Computational Engineering and Science (ICES), UT Austin for hospitality during his sabbatical stay from February to July, 2013.

Domaines: Equations aux dérivées partielles [math.AP]; Matériaux et structures en mécanique [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Andro Mikelic, M.F. Wheeler, Thomas Wick. A quasistatic phase field approach to pressurized fractures . Nonlinearity, 2015, 28, pp.1371-1399. ⟨10.1088/0951-7715/28/5/1371⟩. ⟨hal-01138344v1⟩