A quasi-static phase-field approach to pressurized fractures

Abstract

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A Phase-Field Method for Propagating Fluid-Filled Fractures Coupled to a Surrounding Porous Medium

“…Summarizing and with regard to the existing studies presented in [37,45], the present paper presents two novelties:…”

“…Another method of recent research is peridynamics, which is employed to study pressurized and fluid-filled fractures [30]. To the best of our knowledge, the previously mentioned phase-field approach was first applied to pressurized cracks in [6], and a rigorous model investigation was first undertaken in [36,37]. In these models, the irreversibility condition for crack growth is of crucial importance.…”

“…Our model consists of the fixed-stress split of the Biot equations, with the phase-field regularization in the mechanics part, which has been introduced in [36,37]. In this splitting, we first solve the "fixed stress" [35,41] for the pressure.…”

“…The constraint ∂ t ϕ ≤ 0 is handled using penalization. Detailed explanations of the equations are provided in [36,37,38].…”

A non-intrusive global/local approach applied to phase-field modeling of brittle fracture

“…We mention the papers by Amor et al [7], Miehe et al [8,9], Kuhn and Müller [10], Pham et al [11], Borden et al [12], Mesgarnejad et al [13], Kuhn et al [14], Ambati et al [15], Wu et al [16], where various formulations are developed and validated. Recently, the framework has been also extended to ductile (elasto-plastic) fracture [17][18][19][20][21][22], pressurized fracture in elastic and porous media [23,24], fracture in films [25] and shells [26][27][28], and multi-field fracture [29][30][31][32][33][34][35][36]. Non-intrusive global/local approaches have also been applied to a quite large number of situations: the computation of the propagation of cracks in a sound model using the extended finite element method (XFEM) [37], the computation of assembly of plates introducing realistic non-linear 3D modeling of connectors [38], the extension to non-linear domain decomposition methods [39] and to explicit dynamics [40,41] with an application to the prediction of delamination under impact using Abaqus [42].…”