  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 visco-elastic bodies and rely on a conventional concept of
weak solution and needs no auxiliary interfacial variable. This model is
directly related to a usual phenomenological model of interface fracture by
Hutchinson and Suo 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 (BEM) 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.
