XFEM with NURBS in crack mode I

This research is a first step into coupling the eXtended Finite Element Methods (XFEM) with Non Uniform Rational B-Splines (NURBS). NURBS have been widely used in Computer-Aided Design (CAD) for decades because they are suitable for representing accurately real shapes like circles with only few points. With aim of simplifying the meshing process and probably soon computing directly the CAD geometry, NURBS tends to be used as well for computation [1]; plus they presents an higher regularity particularly suitable for most computational applications. The XFEM [2] is the main alternative to compute strong and weak discontinuities with incompatible meshs. For the purpose of computing crack with NURBS, the XFEM has to be extended again. Enriching the NURBS continuous solution with the Heaviside function H, and the theoretical field close to the tip in crack mode I u ¥I (r;q) leads to equation 1. u =Â A NA(s)qA+Â A0 H(s)NA 0(s)e qA 0 +Â A00 u ¥I (r;q)NA 00(s)KI (1)