Improvements of explicit crack surface representation and update within the generalized finite element method with application to three‐dimensional crack coalescence

Garzon, Jorge L.; O׳Hara, Patrick J.; Duarte, C. Armando; Buttlar, William G.

doi:10.1002/nme.4573

Cited by 36 publications

(27 citation statements)

References 79 publications

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“…This is particularly important in the class of problems considered here because the initial crack surface grows in size by orders of magnitude. Details on these algorithms for geometrical crack surface updating and remeshing are described in . After updating the geometrical crack surface, the 3D GFEM mesh is unrefined to the initial mesh provided by the user. The algorithm is then repeated.…”

Section: Crack Propagation Algorithmmentioning

confidence: 99%

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Gupta

Duarte

2014

Num Anal Meth Geomechanics

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153

131

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SUMMARYHydraulic fracturing is the method of choice to enhance reservoir permeability and well efficiency for extraction of shale gas. Multi‐stranded non‐planar hydraulic fractures are often observed in stimulation sites. Non‐planar fractures propagating from wellbores inclined from the direction of maximum horizontal stress have also been reported. The pressure required to propagate non‐planar fractures is in general higher than in the case of planar fractures. Current computational methods for the simulation of hydraulic fractures generally assume single, symmetric, and planar crack geometries. In order to better understand hydraulic fracturing in complex‐layered naturally fractured reservoirs, fully 3D models need to be developed. In this paper, we present simulations of 3D non‐planar fracture propagation using an adaptive generalized FEM. This method greatly facilitates the discretization of complex 3D fractures, as finite element faces are not required to fit the crack surfaces. A solution strategy for fully automatic propagation of arbitrary 3D cracks is presented. The fracture surface on which pressure is applied is also automatically updated at each step. An efficient technique to numerically integrate boundary conditions on crack surfaces is also proposed and implemented. Strongly graded localized refinement and analytical asymptotic expansions are used as enrichment functions in the neighborhood of fracture fronts to increase the computational accuracy and efficiency of the method. Stress intensity factors with pressure on crack faces are extracted using the contour integral method. Various non‐planar crack geometries are investigated to demonstrate the robustness and flexibility of the proposed simulation methodology. Copyright © 2014 John Wiley & Sons, Ltd.

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Section: Crack Propagation Algorithmmentioning

confidence: 99%

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Gupta

Duarte

2014

Num Anal Meth Geomechanics

Self Cite

153

131

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“…In this paper, we use surface meshes composed of flat triangles (facets) to represent the geometry and handle updates of 3‐D fracture surfaces. Fracture growth is achieved by the addition of triangles or the stretching of the fracture front vertices . The fracture surface mesh has no degrees of freedom and is independent of the 3‐D GFEM mesh used to solve the problem.…”

Section: Generalized Finite Element Methods For 3‐d Fracturesmentioning

confidence: 99%

“…Fracture growth is achieved by the addition of triangles or the stretching of the fracture front vertices. 36 The fracture surface mesh has no degrees of freedom and is independent of the 3-D GFEM mesh used to solve the problem. An example is shown in Figure 1.…”

Section: Geometrical Fracture Surfacesmentioning

confidence: 99%

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

Gupta

Duarte

2017

Num Anal Meth Geomechanics

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SummaryThis paper presents an algorithm and a fully coupled hydromechanical-fracture formulation for the simulation of three-dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3-D fracture front at every fracture propagation step.A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time-dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3-D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.

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“…For XFEM/GFEM applications, the subdivision of the 3D solid elements needs to be performed for the integration purpose. Both relies on well-developed meshing/re-meshing packages [93,94]. The explicit representation of the crack surfaces by triangulation has been used in meshfree methods as well [34,1,36].…”

Section: Crack Growthmentioning

confidence: 99%

“…One approach to alleviate this is to abandon the branch enrichment [1,36]. As a remedy, the crack fronts need to be smoothed through some numerical techniques [93,94]. Similar scenarios occur in Lagrange based BEM for fracture modeling.…”

Section: Crack Growthmentioning

confidence: 99%

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

Peng

Atroshchenko

Kerfriden

et al. 2017

Computer Methods in Applied Mechanics and Engineering

202

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Highlights• We implement an isogeometric BEM routine for fracture by use of dual boundary integral equations.• We propose a singular integration scheme to improve the quadrature accuracy for elements with high aspect ratios.• We investigate the approaches to compute stress intensity factors based on a NURBS representation of the crack surfaces.• We outline a geometric algorithm to propagate the crack based on the fatigue Paris law. AbstractWe present a novel numerical method to simulate crack growth in 3D, directly from the Computer-Aided Design (CAD) geometry of the component, without any mesh generation. The method is an isogeometric boundary element method (IGABEM) based on non-uniform rational B-splines (NURBS). NURBS basis functions are used for the domain and crack representation as well as to approximate the physical quantities involved in the simulations. A stable quadrature scheme for singular integration is proposed to enhance the robustness of the method in dealing with highly distorted elements. Convergence studies in the crack opening displacement is performed for a penny-shaped crack and an elliptical crack. Two approaches to extract stress intensity factors (SIFs): the contour M integral and the virtual crack closure integral are compared using dual integral equations. The results show remarkable accuracy in the computed SIFs, leading to smooth crack paths and reliable fatigue lives, without requiring the generation of any mesh from the CAD model of the component under consideration.

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Improvements of explicit crack surface representation and update within the generalized finite element method with application to three‐dimensional crack coalescence

Cited by 36 publications

References 79 publications

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Simulation of non‐planar three‐dimensional hydraulic fracture propagation

Coupled hydromechanical‐fracture simulations of nonplanar three‐dimensional hydraulic fracture propagation

Isogeometric boundary element methods for three dimensional static fracture and fatigue crack growth

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