A boundary element method for two dimensional linear elastic fracture analysis

A boundary element method is developed for the analysis of fractures in two-dimensional solids. The solids are assumed to be linearly elastic and isotropic, and both bounded and unbounded domains are treated. The development of the boundary integral equations exploits (as usual) Somigliana's identity, but a special manipulation is carried out to ‘regularize’ certain integrals associated with the crack line. The resulting integral equations consist of the conventional ordinary boundary terms and two additional terms which can be identified as a distribution of concentrated forces and a distribution of dislocations along each crack line. The strategy for establishing the integral equations is first outlined in terms of real variables, after which complex variable techniques are adopted for the detailed development. In the numerical implementation of the formulation, the ordinary boundary integrals are treated with standard boundary element techniques, while a novel numerical procedure is developed to treat the crack line integrals. The resulting numerical procedure is used to solve several sample problems for both embedded and surface-breaking cracks, and it is shown that the technique is both accurate and efficient. The utility of the method for simulating curvilinear crack propagation is also demonstrated.