A boundary element implementation for fracture mechanics problems using generalised Westergaard stress functions

In the traditional boundary element methods, the numerical modelling of cracks is usually carried out by means of a hypersingular fundamental solution, which involves a 1=r² kernel for two-dimensional problems. A more natural procedure should make use of fundamental solutions that represent the square root singularity of the gradient field around the crack tip (a Green’s function). Such a representation has been already accomplished in a variationally based framework that also addresses a convenient means of evaluating results at internal points. This paper proposes a procedure for the numerical simulation of two-dimensional problems with a fundamental solution that can be in part or for the whole structure based on generalised Westergaard stress functions. Problems of general topology can be modelled, such as in the case of unbounded and multiply-connected domains. The formulation is naturally applicable to notches and generally curved cracks. It also provides an easy means of evaluating stress intensity factors, when particularly applied to fracture mechanics. The main features of the theory are briefly presented in the paper, together with several validating examples and some convergence assessments.