Mesh-size-objective XFEM for regularized continuous–discontinuous transition

The focus is on a Regularized eXtended Finite Element Model (REXFEM) for modeling the transition from a local continuum damage model to a model with an embedded cohesive discontinuity. The discontinuity surface and the displacement jump are replaced by a volume, whose width depends on a regularization length, and by a regularized jump function, respectively. By exploiting the property that the stress–strain work spent within the regularized discontinuity, for vanishing regularization, is equivalent to the traction–separation work dissipated in a zero-width discontinuity surface, a mesh-size independent transition from the continuous displacement regime to the discontinuous displacement regime is obtained. Sub-elemental enrichment is considered, leading to a localization band restricted to a single layer of finite elements, like in the smeared-crack approach. Therefore, a comparison in the two-dimensional case with a literature model and with a commercial code which are based on the smeared-crack approach is presented.

► The proposed formulation (Re-XFEM is a simple, regularized version of the eXtended Finite Element Method (XFEM).
► Unlike existing formulations, Re-XFEM implies smooth transition, i.e. no loss of structural stiffness occurs.
► Re-XFEM makes it possible to preserve mesh-independent results.
► Re-XFEM leads to better results than smeared crack approach, because the crack dofs are nodal according to standard XFEM.