On the computation of two‐dimensional stress intensity factors using the boundary element method

Abstract

SUMMARYGeneral two-dimensional linear elastic fracture problems are investigated using the boundary element method. The displacement and 1/& traction behaviour near a crack tip are incorporated in special crack elements. Stress intensity factors of both modes I and I1 are obtained directly from crack-tip nodal values for a variety of crack problems, including straight and curved cracks in finite and infinite bodies. A multidomain approach is adopted to treat cracks in an infinite body. The body is subdivided into two regions: an infinite part with a finite hole and a finite inclusion. Numerical results, compared with exact solution whenever possible, are accurate even with a coarse discretization.

Boundary integral equation fracture mechanics analysis of plane orthotropic bodies

“…Indeed Martinez and Dominguez [16] demonstrated that using this latter traction result approach, the stress intensity factor solutions are quite insensitive to the element size distribution of the boundary element mesh, at least for isotropic materials, and accurate results can be obtained with coarse mesh discretisations. A similar finding was reported by Jia et al [17] in their BIE fracture mechanics study, although the traction singular crack-tip element used is based on the ordinary mid-point type. The present authors extended the use of these quarter-point singular elements in the BIE method to treating interface cracks between dissimilar isotropic materials [18] [21].…”

Stress intensity factor computation using the method of fundamental solutions

“…Such splitting (sometimes called "stitching") has been used before for crack problems, using boundary element methods [23,24]. As a result, the crack has two faces, and the displacement near one face (in Ω 1 , say; see Figure 1) can be represented by fundamental solutions near the other face (in Ω 2 ): the numerical approximation can be improved by increasing N .…”

Stress intensity factor computation using the method of fundamental solutions: mixed‐mode problems

“…The second method utilized domain decomposition. Such splitting (sometimes called 'stitching') has been used before for crack problems, using boundary element methods [23,24]. As a result, the crack has two faces, and the displacement near one face (in 1 , say; see Figure 1) can be represented by fundamental solutions near the other face (in 2 ): the numerical approximation can be improved by increasing N .…”