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. (C) 2016 Elsevier Ltd. All rights reserved.