Weakly singular BIEM for analysis of cracks embedded in symmetric elastic whole space

Abstract

In this paper, a weakly singular boundary integral equation method is developed for the stress analysis of an anisotropic, linearly elastic, cracked whole space possessing a plane of symmetry. This study should offer an alternative powerful tool essential for the modeling of both near-surface and deeply embedded defects in a rock/soil medium. A system of governing equations is established using a pair of weakly singular, weakform, displacement and traction integral equations for the cracked whole space along with the symmetric condition. The final equations contain only unknown crack-face data in a lowerhalf of the whole space. In addition to their capability to treat cracks of arbitrary shape, material anisotropy and general loading conditions, all involved kernels are weakly singular allowing all integrals to be interpreted in the sense of Riemann. A symmetric Galerkin boundary element method together with the Galerkin approximation is implemented to solve the governing integral equations for the unknown crack-face data. To further enhance the accuracy and efficiency of the proposed scheme, special basis functions are introduced to approximate the near-front field and the interpolation technique is adopted to evaluate all kernels for generally anisotropic materials. The solved crack-face displacement data is then utilized to postprocess for the essential fracture information along the crack front. Various scenarios are employed to verify the proposed technique and a selected set of results is presented to demonstrate its accuracy and computational robustness.