A Regularized XFEM model for transition from continous to discontinous displacement

A continuum two-fields extended finite element formulation enriched with a regularization length is presented. By extending the mechanical framework for elastic interfaces proposed in [Benvenuti et al. 2007], the geometrical discontinuity is replaced by a regularized layer with an elastodamaging behavior. Salient features of the proposed methodology are that a continuum cohesive-like stress field and a “bridging” stress field emerge, while the cohesive traction-separation work is proved to be recovered when the regularization length vanishes.