Two adhesive-contact models for quasistatic mixed-mode delamination problems

Two models for quasistatic adhesive unilateral contact delaminating in mixed fracture mode, i.e. distinguishing the less-dissipative mode I (opening) from the more-dissipative mode II (shearing), and allowing rigorous mathematical and numerical analysis, are studied. One model, referred to as associative plasticity-based rate-independent model (APRIM), works for purely elastic bodies and involves, in addition to an interface damage variable, an auxiliary variable (representing interfacial plastic slip) to provide a fracture-mode sensitivity. It relies on a particular concept of force-driven local solutions (given by either vanishing-viscosity concept or maximum-dissipation principle). The other model, referred to as linear elastic–(perfectly) brittle interface model (LEBIM), works for visco-elastic bodies and relies on a conventional concept of weak solution and needs no auxiliary interfacial variable. This model is directly related to a usual phenomenological model of mixed-mode dependent interface fracture used in engineering. This paper devises a way how the phenomenology of the LEBIM can be fit to imitate the APRIM under relatively very slow loading, where both models are essentially rate-independent. The so-called effective dissipated energy is partitioned in both formulations to the surface energy and the energy dissipated during the interface debonding process, where the former is independent and the latter dependent on the fracture mode mixity. A numerical comparison of these models, implemented in a boundary element method code, is carried out on a suitable two-dimensional example. Furthermore, the computational efficiency and behaviour of the LEBIM is illustrated on another geometrically more complicated numerical example.