The singular function boundary integral method for a two-dimensional fracture problem

The singular function boundary integral method (SFBIM) originally developed for Laplacian problems with boundary singularities is extended for solving two-dimensional fracture problems formulated in terms of the Airy stress function. Our goal is the accurate, direct computation of the associated stress intensity factors, which appear as coefficients in the asymptotic expansion of the solution near the crack tip. In the SFBIM, the leading terms of the asymptotic solution are used to approximate the solution and to weight the governing biharmonic equation in the Galerkin sense. The discretized equations are reduced to boundary integrals by means of Green's theorem and the Dirichlet boundary conditions are weakly enforced by means of Lagrange multipliers. The numerical results on a model problem show that the method converges extremely fast and yields accurate estimates of the leading stress intensity factors.