Extended isogeometric analysis of a progressively fracturing fluid‐saturated porous medium

Abstract

An extended isogeometric analysis (XIGA) approach is proposed for modeling fracturing in a fluid-saturated porous material. XIGA provides a definition of the discontinuity independent of the underlying mesh layout, which obviates the need of knowing the crack extension direction a priori. Unlike Lagrange shape functions used in the standard finite element approach, non-uniform rational B-splines (NURBS) provide a higher-order interelement continuity which leads to a continuous fluid flow also at element boundaries, thereby satisfying the local mass balance. It also leads to an improved estimate of the crack path due to a smoother stress distribution. The NURBS basis functions are cast in finite element data structure using Bézier extraction. To model the discontinuity, the Heaviside sign function is utilized within the displacement and the pressure fields, complemented by the shifting and the blending techniques to enforce compatibility perpendicular and parallel to the crack path, respectively. Different aspects of the approach are assessed through examples comprising straight and curved crack paths for stationary and propagating discontinuities. K E Y W O R D Scohesive fracture, extended finite element method, fluid flow, isogeometric analysis, porous

Analysis of progressive fracture in fluid‐saturated porous medium using splines

“…The curve exhibits structural softening due to progressive crack propagation. In the figure, a close agreement is observed between the two discretizations 8 …”

“…The fluid flows from 8) is used with the tensile strength t u = 2.7 MPa and fracture energy  c = 0.095 N/mm. We only consider mode-I fracture, that is, d int = 0 in Equation (8). To avoid interpenetration, a penalty stiffness k p = 10 10 MPa/mm is specified in the normal direction of the crack opening.…”

“…In the figure, a close agreement is observed between the two discretizations. 8 Figure 8B presents the pressure p + along the top crack interface Γ + c after the crack is fully developed along the middle plane of the plate. In addition, a comparison between the two discretizations is given for the fluid pressure p + here.…”

“…The accuracy of the stress prediction and the pore pressure evaluation are particularly important, also in relation to the local mass conservation between elements. The extended isogeometric method (XIGA) avoids the stress and pore pressure gradient inaccuracy issue 8 . However, to confine the influence of cracks locally, ‐lines must be added in cracked elements 21 .…”

Hydraulic fracturing analysis in fluid‐saturated porous medium

“…The first numerical model of the fluid flow in a porous medium with a discontinuity was done by Boone and Ingraffea, 3 using finite elements for the porous medium and finite differences for the fluid in the crack. Since then a host of numerical models have been proposed, such as finite elements, 4 the extended finite element method, [5][6][7] isogeometric analysis, 8 extended isogeometric analysis, 9 embedded strong discontinuities, 10 the phase-field method, 11 a coupled finite element-peridynamics model, 12 interfaces elements equipped with a cohesive zone model 13 and a combined finite-discrete element method. 14 Due to their simplicity and robust performance interface elements have gained popularity for modelling fracture initiation and propagation in a poroelastic medium.…”