An integration technique for 3D curved cracks and branched discontinuities within the extended Finite Element Method

In this paper, we present a robust procedure for the integration of discontinuous functions across arbitrary curved interfaces defined by means of level set functions for an application to linear and quadratic eXtended Finite Elements. It includes the possibility of having branched discontinuities. For the volume integration, integration subcells are built inside the approximation mesh. The set of subcells conforms to the discontinuities, constitutes the integration mesh and can also be used by the visualization tools. Surface integration may also be performed along the crack faces by selecting the appropriate subcell faces. When combined with the eXtended Finite Element Method (XFEM) optimal convergence rates are obtained with curved geometries for both linear and quadratic elements.