Extended Finite Element Method for hygro‐mechanical analysis of crack propagation in porous materials

Abstract

In computational structural analyses, strong discontinuities, such as propagating cracks in concrete structures, joints in rocks or shear bands in soft soils, the highly accelerated moisture transport in the opening discontinuities has to be taken into account. The paper is concerned with an Extended Finite Element model for the numerical representation of crack propagation in partially saturated porous materials. Based on an extended variational formulation for the simulation of moisture transport in cracks, enhanced approximations of the displacement field and the moisture flux across the discontinuity are adopted. Model descriptionDiscontinuities, such as propagating cracks, are characterized by a disturbance of the overall distribution of the field variables within a very small length. To resolve the small and the large scale portion of the solution, the Extended Finite Element method [4], exploiting the Partition of Unity property of shape functions, offers the possibility to include arbitrary enhancement functions into the finite element approximation to improve the local approximation of non-smooth distributions of field variables, such as discontinuities of the displacement field or the fluid pressure field across cracks [3,5]. For an element fully crossed by a crack, the Sign function is used for the representation of the discontinuous displacement field across the crack.where n r is the number of nodes used for the spatial discretization of the regular displacement field (superscript r). In coupled hygro-mechanical problems, involving porous materials with cracks, the flow of the pore fluid across the crack will be discontinuous (Fig.1). Adopting poromechanics as the modeling framework, and assuming pores to be filled by an ideal mixture of water vapor and dry air (subscript g), the two-field problem is characterized by the displacement field u and the capillary pressure p c as degrees of freedom. Considering a jump of the moisture flux across the discontinuity denoted by ∂ S leads to the weak form of the mass balanceConsidering the local mass balance at the discontinuity (i.e. on the small scale level) provides the normal component of the moisture flux across the crack as q * n = n S · q l,∂ S Ω = w ρ

Numerical modeling of non-planar hydraulic fracture propagation in brittle and ductile rocks using XFEM with cohesive zone method

“…A key advantage of XFEM is that in such problems the finite element mesh does not need to be updated to track the crack path, and discontinuous enrichment functions are used to approximate the displacement discontinuity across the crack surface, which significantly reduced the computational costs and projection errors associated with conventional finite element methods that restricting the discontinuities to mesh edges (Karihaloo and Xiao, 2003). Since the introduction of this method, the XFEM has been used to model complex, non-planar hydraulic fracture propagations by many authors (Lecampion, 2009;Dahi-Taleghani and Olson, 2011;Meschke and Leonhart, 2011;Gordeliy and Peirce, 2013).…”

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

“…hydraulic fracture propagation in fluid-saturated porous media are presented in the works of Rńethoré et al [40] and Irzal et al [41]. Related works are presented in the papers by Leonhart and Meschke [42] and Watanabe et al [43]. Most hydraulic fracture models are based on linear elastic fracture mechanics (LEFM) [44].…”

“…XFEM formulations for the simulation of hydraulic fracture propagation in fluid‐saturated porous media are presented in the works of Rńethoré et al and Irzal et al . Related works are presented in the papers by Leonhart and Meschke and Watanabe et al .…”

Effects of Intrinsic Properties on Fracture Nucleation and Propagation in Swelling Hydrogels

“…Wells and Sluys [11] incorporated a cohesive surface formulation into the method to achieve the crack propagation in any arbitrary direction. Similarly, Leonhart and Meschke took the moisture transport in opening discontinuities into account and analysed the crack propagation in partially saturated porous media [12]. Kraaijeveld et al [13] took osmotic forces into consideration and studied Mode I crack propagation in saturated ionized porous media in small deformations.…”