On the elimination of quadrature subcells for discontinuous functions in the eXtended Finite-Element Method

The introduction of discontinuous/non-differentiable functions in the eXtended Finite-Element Method allows to model discontinuities independent of the mesh structure. However, to compute the stiffness matrix of the elements intersected by the discontinuity, a subdivision of the elements into quadrature subcells aligned with the discontinuity line is commonly adopted. In the paper, it is shown how standard Gauss quadrature can be used in the elements containing the discontinuity without splitting the elements into subcells or introducing any additional approximation. The technique is illustrated and developed in one, two and three dimensions for crack and material discontinuity problems.