A comparative assessment of coupled cohesive zone models for modeling of mixed-mode debonding and contact

Due to its simplicity, cohesive zone modeling is largely used for a variety of applications, including fracture of ductile and brittle solids, delamination in composites at the micro- or macro- scale, and behaviour of adhesive layers. Both uncoupled and coupled cohesive zone approaches have been used in the literature for modeling of interfaces under mixed-mode conditions. In uncoupled models, cohesive laws in the normal and tangential directions are independent from each other. A mixed-mode fracture criterion may or may not be introduced. In coupled models, cohesive laws in the normal and tangential directions are linked to each other, typically by means of a coupling parameter. Also in this case a further distinction can be made between approaches in which the cohesive laws are or not derived from a potential. The lack of a potential allows for different fracture energies in different mode mixities. Also, it introduces a path-dependency, which has a physical ground considering that cohesive zone models can describe an irreversible damage process at an interface. In the current literature, a few coupled cohesive zone models are available. Having been developed for a diverse set of applications, they differ in several aspects, including the presence of a potential, the shape of the laws, the definition of the coupling parameter, and the unloading paths. The relative performance of these models is currently not clear, and therefore their suitability to any specific application needs to be comparatively assessed. In this paper, the available models are implemented by means of a node-to-segment contact element, suitably generalized to incorporate tension forces. This element is then used to represent the interface between a thin bonded plate and a quasi-brittle substrate. The main application of reference is the interface between fiber-reinforced polymer thin sheets and concrete or masonry substrates, which can be subjected to mixed-mode loading as a result of geometry or loading configuration. The most suitable model for this interface is identified, and its predictions of the interfacial behavior under some significant loading schemes are compared with previous analytical and experimental results.