An extended finite element method (XFEM) for linear elastic fracture with smooth nodal stress. (15th January 2017) - Peng, X.; Kulasegaram, S.; Wu, S.C.; Bordas, S.P.A.
Highlights: A nodal C 1 approximation procedure combined with partition of unity enrichment has been constructed for fracture. The double-interpolation approximation improves the accuracy of the solution field by up to one order of magnitude with the same degrees of freedom as the constant strain triangular element. The double-interpolation approximation is able to calculate the stress at node directly through interpolation. The enriched form of the double-interpolation approximation enables a way to propagate the crack with minimal remeshing with a smoother crack tip stress field obtained. Abstract: We present a method to achieve smooth nodal stresses in the XFEM. The salient feature of the method is to introduce an 'average' gradient into the construction of the approximation. Due to the higher-order polynomial basis provided by the interpolants, the new approximation enhances the smoothness of the solution without requiring an increased number of degrees of freedom. We conclude from numerical tests that the proposed method tends to be an efficient alternative to the classical XFEM, bypassing any postprocessing step to obtain smooth nodal stress fields and providing a direct means to compute local stress error measures.