An analytical method, based upon the use of a continuous distribution of dislocations to model curved cracks in solids of arbitrarily shaped finite geometries, was presented. The boundary of the finite body, and the curved crack, were modelled by distributed dislocations. The influence function of the dislocation, along the finite-body boundary, was reduced to a product of the Hilbert kernel with a normal function. The influence function for curved cracks was reduced to the product of a Cauchy kernel and a normal function. This resulted in a system of singular integral equations. By using the order-decreasing method, the system was reduced to normal integral equations; which were then solved numerically.

Modelling Cracks in Arbitrarily Shaped Finite Bodies by Distribution of Dislocation. J.J.Han, M.Dhanasekar: International Journal of Solids and Structures, 2004, 41[2], 399-411