Applications of SGBEM for analysis of 3D cracks in general anisotropic linear elastic multi-regions

Abstract

In this paper, we present a computation procedure based upon the weakly-singular, symmetric Galerkin boundary element method (SGBEM) for analysis of three dimensional cracks in anisotropic multi-regions consisting of sub-domains made from different materials. The symmetric weak-form, governing the integral equation of the boundary value problem is obtained by employing a suitable combination of the weakly-singular, weak-form displacement and traction integral equations for each sub-domain. This set of integral equations is applicable for modeling cracks in both isotropic and general anisotropic media. The final governing integral equation possesses important features including that it is in a symmetric form, it contains only weakly-singular kernels of order 1/r, it is applicable for modeling both embedded and surface breaking cracks subjected to arbitrary mixed-mode loading and it can be used to treat cracks in a domain consisting of several subregions with different material properties. In the numerical implementation, special crack tip elements are utilized along the crack front and this allows the fracture information (viz. stress intensity factors) to be determined directly and accurately in terms of special DOFs associated with nodes along the crack front. Two numerical examples are presented to illustrate convergence, accuracy and robustness of the technique.