H.C. Andrade, J. Trevelyan, E.D. Leonel

A new extended isogeometric boundary element method (XIGABEM) formulation is proposed for simulating multiple fatigue crack propagation in two-dimensional domains. The classical use of NURBS in isogeometric formulations is further extended by repeated knot insertion to introduce a ${C}^{-1}$ continuity within the approximation space as an elegant approach to representing geometrical discontinuities at crack intersections. This strategy is also used to restrict the enrichment term to the portion of the NURBS defining the tip, where it is necessary. At this near-tip zone, the linear elastic fracture mechanics solutions are embedded into the displacement approximation to represent the theoretical square root behaviour. The enrichment procedure introduces just two degrees of freedom per crack tip, and a tying constraint is used to yield a square linear system. In this *direct* approach, the stress intensity factors (SIFs) are found as terms in the solution vector without requiring post-processing techniques.

Several examples are presented to illustrate the application of the XIGABEM. The accuracy of the results compares favourably against those from the literature, and also against solutions obtained from unenriched and enriched indirect methods that employ the J-integral for SIF extraction. Furthermore, the proposed direct approach is capable of significantly reducing the execution time.