Mikelić, Andro; Wheeler, Mary F.; Wick, Thomas A quasi-static phase-field approach to pressurized fractures. (English) Zbl 1316.35287 Nonlinearity 28, No. 5, 1371-1399 (2015). Summary: 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. Cited in 48 Documents MSC: 35Q86 PDEs in connection with geophysics 47J20 Variational and other types of inequalities involving nonlinear operators (general) 49J40 Variational inequalities 74R10 Brittle fracture 86A99 Geophysics Keywords:pressurized fractures; phase-field; quasi-static model; incremental formulation; Biot’s consolidation equations PDFBibTeX XMLCite \textit{A. Mikelić} et al., Nonlinearity 28, No. 5, 1371--1399 (2015; Zbl 1316.35287) Full Text: DOI HAL