An integral equations method for solving the problem of a plane crack of arbitrary shape

Bui, Huy Duong

doi:10.1016/0022-5096(77)90018-7

Cited by 177 publications

(103 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Bui (1977), Weaver (1977), Lin'kov and Mogilevskaya (1986), Luchi and Rizzuti (1987), Kuriyama and Mizuta (1993), Chen and Gross (1997), Chen and Lee (2001), Frangi et al (2002), Lo et al (2005). There are also various papers on three-dimensional crack propagation, e.g.…”

Section: Literature Reviewmentioning

confidence: 99%

“…For the specimens to be water-saturated, a viton membrane is used to prevent polyurethane penetration into the rock. The specimen is placed on a lower loading platen (2) and confined laterally by a biaxial frame (3) in the form of a thick-walled cylinder. A pair of equally angled wedges allowing a tolerance of 0.5 mm in specimen width is used for fitting the specimen within the biaxial frame (Fig.…”

Section: Plane-strain Apparatusmentioning

confidence: 99%

See 1 more Smart Citation

Geomechanical Simulation of Fluid-Driven Fractures

Makhnenko¹,

Nikolskiy²,

Mogilevskaya³

et al. 2012

View full text Add to dashboard Cite

The project supported graduate students working on experimental and numerical modeling of rock fracture, with the following objectives: (a) perform laboratory testing of fluid-saturated rock; (b) develop predictive models for simulation of fracture; and (c) establish educational frameworks for geologic sequestration issues related to rock fracture. These objectives were achieved through (i) using a novel apparatus to produce faulting in a fluid-saturated rock; (ii) modeling fracture with a boundary element method; and (iii) developing curricula for training geoengineers in experimental mechanics, numerical modeling of fracture, and poroelasticity.4 EXECUTIVE SUMMARYCarbon storage technologies offer a means of reducing CO 2 emissions and mitigating climate change. These new technologies will require a workforce educated in geomechanics. To this end, the project supported graduate students working on geomechanical simulation of fluid-driven fractures with the following objectives:1. Measure elastic and inelastic response of fluid-saturated rock 2. Develop predictive models for simulation of fluid-driven fractures 1. Deformation and damage of a porous, fluid-saturated rock under drained and undrained conditions were investigated. A plane-strain apparatus was modified in order to conduct tests with water-saturated rock specimens and to measure the pore pressure within the rock. Transducers within the apparatus were calibrated at the various loading states and the compliances of the system were determined. Plane strain compression and conventional triaxial compression tests were performed at different confining pressures under air-dry, drained, and undrained conditions. The behavior of the rock was evaluated within the framework of linear poroelasticity. Dilatant hardening and contractant softening was investigated from undrained experiments, where pore pressure was measured throughout the failure process. The parameters that govern the inelastic deformation of fluid-saturated rock, i.e. dilatancy angle β, friction coefficient µ, poroelastic coefficient K eff , shear modulus G, and inelastic hardening modulus H, were calculated for the drained response. The constitutive model predicts the undrained inelastic response of the rock fairly well, almost up to the peak load if compared with the undrained test that had the same effective mean stress at the onset of inelasticity. Knowledge of dilatant hardening behavior is essential for the proper assessment of underground structures, such as long-term CO 2 storage facilities.2. The boundary element method (BEM) is based on the boundary integral representation equivalent to the differential equation governing a specific physical problem. Such representation is possible when the so-called fundamental solution of the governing differential equation is available. The fundamental solution satisfies the differential equation everywhere in the domain except one point where it is singular. In the case of linear isotropic and homogeneous elasticity, the fundamental solution...

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Plane-strain Apparatusmentioning

confidence: 99%

Geomechanical Simulation of Fluid-Driven Fractures

Makhnenko¹,

Nikolskiy²,

Mogilevskaya³

et al. 2012

View full text Add to dashboard Cite

show abstract

“…This in turn requires C 1,α regularity of the density (usually the displacement discontinuity) at the collocation points and specially designed singular integration procedures, making the implementation of traction CBIEs quite involved. In contrast, the symmetric Galerkin BIE (SGBIE) approach to crack problems only requires H 1/2 densities for the continuous problem, making C 0 boundary element interpolations suitable (see [12] for an early implementation of the latter approach for plane cracks, and also [21,22,19,8,28], among many references on this treatmnent). Moreover, SGBEM is based on a variational (weak) version of the integral equations, thus with n denoting the outward unit normal to Ω.…”

Section: Introductionmentioning

confidence: 99%

“…In such cases, cracks are directly represented as displacement discontinuity loci and the traction integral equation is employed to enforce static conditions on the crack faces and permit single-domain formulations irrespective of the number of cracks involved, see e.g. [12,17] for early expositions of these ideas. However, traction collocation BIE formulations, whether employed in isolation or as a component of the so-called dual approach [30], involve an hypersingular kernel.…”

Section: Introductionmentioning

confidence: 99%

Fast multipole method applied to Symmetric Galerkin boundary element method for 3D elasticity and fracture problems

Pham¹,

Mouhoubi²,

Bonnet³

et al. 2012

Engineering Analysis with Boundary Elements

View full text Add to dashboard Cite

“…The singularity of integral kernels can be reduced if the technique of integration by parts is employed. Some research works in this area have already been carried out [5,[11][12][13]. Within the scope of BEM for the fracture analysis of anisotropic piezoelectric materials, some studies [14][15][16][17][18][19] have been published in the past, but most of these works are based on the displacement BIE and are only suitable for simple problems.…”

Section: Introductionmentioning

confidence: 99%

Boundary element‐free method for fracture analysis of 2‐D anisotropic piezoelectric solids

Liew

Sun

Kitipornchai

2006

Numerical Meth Engineering

View full text Add to dashboard Cite

SUMMARYThis paper considers a 2-D fracture analysis of anisotropic piezoelectric solids by a boundary elementfree method. A traction boundary integral equation (BIE) that only involves the singular terms of order 1/r is first derived using integration by parts. New variables, namely, the tangential derivative of the extended displacement (the extended displacement density) for the general boundary and the tangential derivative of the extended crack opening displacement (the extended displacement dislocation density), are introduced to the equation so that solution to curved crack problems is possible. This resulted equation can be directly applied to general boundary and crack surface, and no separate treatments are necessary for the upper and lower surfaces of the crack. The extended displacement dislocation densities on the crack surface are expressed as the product of the characteristic terms and unknown weight functions, and the unknown weight functions are modelled using the moving least-squares (MLS) approximation. The numerical scheme of the boundary element-free method is established, and an effective numerical procedure is adopted to evaluate the singular integrals. The extended 'stress intensity factors' (SIFs) are computed for some selected example problems that contain straight or curved cracks, and good numerical results are obtained.

show abstract

An integral equations method for solving the problem of a plane crack of arbitrary shape

Cited by 177 publications

References 4 publications

Geomechanical Simulation of Fluid-Driven Fractures

Geomechanical Simulation of Fluid-Driven Fractures

Fast multipole method applied to Symmetric Galerkin boundary element method for 3D elasticity and fracture problems

Boundary element‐free method for fracture analysis of 2‐D anisotropic piezoelectric solids

Contact Info

Product

Resources

About