Cohesive zone models (CZMs) which were pioneered by Dugdale and Barrenblatt is a continuation of linear elastic fracture mechanics with which the unrealistic stress singularity ahead the crack tip is avoided. From a numerical point of view, CZMs have been incorporated in a finite element (FE) context using zero-thickness interface elements, elements with embedded discontinuities and elements with discontinuous enrichment via the extended/generalized finite element method (XFEM/ GFEM).  It should be emphasized that the term ‘‘cohesive elements’’ or ‘‘cohesive zone elements’’ usually used to refer to cohesive interface elements is misleading since elements with embedded cohesive cracks or XFEM with cohesive cracks are also cohesive elements. Therefore  the name ‘‘cohesive interface elements’’ is used to indicate interface elements equipped with a cohesive law. A cohesive law provides a relation between the cohesive traction and the displacement jump across the crack surfaces.
 
Despite of the fact that XFEM/GFEM has been gaining more popularity within the fracture mechanics community, interface elements still constitute a very good candidate for modeling a number of fracture mechanics problems including interfacial fracture (delamination in composite laminates, failure of adhesive layers, failure of layered composites  such as fiber-metal laminates matrix/interface debonding in fiber reinforced composites) and problems with complex crack patterns (fragmentation, dynamic crack branching, failure of heterogeneous materials). Cohesive interface elements possess the following advantages: (i) easy incorporation into any FE codes (the volumetric element formulation is unaltered),1 (ii) robustness, (iii) straightforward parallelization and (iv) suitable for modeling pervasive fracture and fragmentation.