A domain decomposition based method for two-dimensional linear elastic fractures

In this study, the two-dimensional physical domain containing cracks is divided into several non-overlapping parts: rectangular crack-tip regions around crack tips and the outer region without any crack tip. In each crack-tip region the displacement is approximated with Williams׳ series; while in the outer region it is approximated with numerical manifold interpolation. In order to balance accuracy and efficiency in solution, a transitional zone encompassing each crack-tip region is locally refined with a structured mesh. To avoid singular integration over a crack-tip region, the potential energy over every crack-tip region is transformed into the boundary integration. Three different methods to enforce compatibility on interfaces are compared, concluding the Lagrange multiplier method is superior over the other two.