Domain and boundary quadrature for enrichment functions in the extended finite element method

The two main properties making the extended finite element method one of the most promising finite element technologies are the possibility for the mesh not to conform to discontinuities and the introduction of arbitrary enrichment functions able to effectively describe the features of the problem being solved. However, non polynomial bases inside the elements require special quadrature techniques, dealing with discontinuities and/or singularities. In the paper a recently proposed technique, based on mapping the enrichment functions onto polynomials, is further developed, with applications to cracks and dislocations. The technique allows to perform standard Gauss quadrature in the enriched elements and the location of the singularity/discontinuity is accounted for in the equivalent polynomial coefficients.