  We present a general energy approach to study the unsteady adhesive contact
of viscoelastic materials. Under the assumption of infinitely short-range
adhesive interactions, we exploit the principle of virtual work to generalize
Griffith's local energy balance at contact edges to the case of a
non-conservative (viscoelastic) material, subjected to a generic contact
time-history. We apply the proposed energy balance criterion to study the
approach-retraction motion of a rigid sphere in contact with a viscoelastic
half-space. A strong interplay between adhesion and viscoelastic hysteretic
losses is reported as the adhesion strength can strongly increase, depending on
the loading history. Two diffrent mechanisms govern the pull-off force increase
during either approachretraction cycles and approach - full relaxation -
retraction tests. In the former case, hysteretic losses occurring close to the
circular perimeter of the contact play the major role, significantly enhancing
the energy release rate required change the contact size. In the latter case,
instead, the pull-off enhancement depends on the glassy response of the whole
material which, triggered by the fast retraction after relaxation, leads to a
sort of `frozen' state and at-punch-like detachment mechanism (i.e., constant
contact area). In this case, the JKR theory of adhesive contact cannot be
invoked to relate the observed pull-off force to the effective adhesion energy,
i.e. the energy release rate G, and strongly overestimates it. Therefore, a
rigorous mathematical procedure is also proposed to correctly calculate the
energy release rate in viscoelastic dissipative contacts.
