On the equivalence between the $$s$$ s -method, the XFEM and the ply-by-ply discretization for delamination analyses of laminated composites

Two hierarchical approaches, the $$s$$ -method and the extended finite element method (XFEM), are compared to the classical ply-by-ply discretization approach in terms of their effectiveness in modeling delamination in laminated composites. In the two hierarchical approaches, a smooth approximation field based on the mesh made of through-the-thickness solid laminated elements is first introduced to resolve a delamination-free response of the composite structure. The initiation and propagation of delamination is modeled by either superposition of element patches (s-method) or by enrichment functions (XFEM). A cohesive zone model is employed to model decohesion at the inter-ply interfaces. In terms of representing strong discontinuities, the two hierarchical methods have been shown to represent an identical approximation space as the classical ply-by-ply discretization approach, even though the s-method gives rise to sparser matrix structure. In terms of representing weak discontinuities, the s-method has been shown to be equivalent to the ply-by-ply discretization approach and provides a seamless transition from weak to strong discontinuity.