Phase-field Modeling of Pressurized Fractures in a Poroelastic Medium
نویسندگان
چکیده
In this paper we present an incremental formulation of the phase field model for a fluid filled crack in a poroelastic medium. The mathematical model represents a linear elasticity system with fading elastic moduli as the crack grows that is coupled with an elliptic variational inequality for the phase field variable. The convex constraint of the variational inequality assures the irreversibility and entropy compatibility of the crack formation. We establish existence of a minimizer of an energy functional of an incremental problem and convergence of a finite dimensional approximation. Computational results of benchmark problems are provided that demonstrate the effectiveness of this approach in treating fracture propagation.
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