  An adhesive unilateral contact between visco-elastic bodies at small strains
and in a Kelvin-Voigt rheology is scrutinized, neglecting inertia. The
flow-rule for debonding the adhesive is considered rate independent,
unidirectional, and non-associative due to dependence on the mixity of modes of
delamination, namely Mode I (opening) needs (=dissipates) less energy than Mode
II (shearing). Such mode-mixity dependence of delamination is a very pronounced
(and experimentally confirmed) phenomenon typically considered in engineering
models.
  An efficient semi-implicit-in-time FEM discretization leading to recursive
quadratic mathematical programs is devised. Its convergence and thus the
existence of weak solutions is proved. Computational experiments implemented by
BEM illustrate the modeling aspects and the numerical efficiency of the
discretization.
