A regularized XFEM model for the transition from continuous to discontinuous displacements

This work focuses on the modelling through the extended finite element method of structural problems characterized by discontinuous displacement. As a model problem, an elastic isotropic domain characterized by a displacement discontinuity across a surface is studied. A regularization of the displacement field is introduced depending on a scalar parameter. The regularized solution is defined in a layer. The emerging strain and stress fields are independently modelled using specific constitutive assumptions. In particular, it is shown that the mechanical work spent within the regularization layer can be interpreted as an interface work provided that a spring-like constitutive law is adopted. The accuracy of the integration procedures adopted for the stiffness matrix is assessed, as highly non-linear terms appear. Standard Gauss quadrature is compared with adaptive quadrature and with a new technique, based on an equivalent polynomial approach. One- and two-dimensional results are reported for varying discretization size, regularization parameter, and constitutive parameters.