  We present a novel theory of the adhesive contact of linear viscoelastic
materials against rigid substrates moving at constant velocity. Despite the
non-conservative behavior of the system, the closure equation of the contact
problem can be rigorously formulated in the form of a local energy balance. In
the case of adhesiveless contacts, this is equivalent to enforce the
stationarity of the total energy stored into the viscoelastic material.
However, in the presence of interfacial adhesion, the appearance of
non-conservative terms leads to different values of the energy release rates G1
and G2 at the contact trailing and leading edges, respectively. Specifically,
the present theory predicts a non-monotonic trend of G1 and G2 as function of
the indenter velocity, as well as a very significant enhancement of hysteretic
friction due to the coupling between adhesion and viscoelasticity, compared to
the adhesiveless case. Both predictions are in very good agreement with
existing experimental data.
