A quasi-static phase-field approach to pressurized fractures. (17th April 2015)

• Record Type: Journal Article
• Authors: Mikelić, Andro; Wheeler, Mary F; Wick, Thomas
• Is Part Of: Nonlinearity. Volume 28:Number 5(2015:May)
• Page Start: 1371
• Page End: 1399
• Publication Date: 2015-04-17
• Subjects: pressurized fractures -- phase field -- quasi-static model -- incremental formulation -- Biot's consolidation equations; 35Q86 -- 47J20 -- 49J40 -- 74R10; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/0951-7715/28/5/1371
• Languages: English
• ISSNs: 0951-7715

Abstract

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.