  In this study, we propose a theory of rough adhesive contact of viscoelastic
materials in steady-state sliding. By exploiting a boundary formulation based
on Green function approach, the unknown contact domain is calculated by
enforcing the local energy balance at the contact edge, thus considering also
the non-conservative work of internal stresses which is directly related to the
odd part of the Green function. Theoretical predictions indicate that
viscoelasticity may enhance the adhesive performance depending on the sliding
velocity, thus leading to larger contact area and pull-off force compared to
the equivalent adhesive elastic case The interplay between viscoelasticity and
adhesion also affects the overall friction. Indeed, at low velocity, friction
is strongly enhanced compared to the adhesiveless viscoelastic case, mainly due
to the small-scale viscoelastic hysteresis induced by the adhesive neck close
to the contact edge At higher velocity, the effect of viscoelastic hysteresis
occurring at larger scales (bulk material) leads to even higher friction. Under
these conditions, in the presence of adhesion, the small-scale and large-scale
viscoelastic contributions to friction cannot be separated. Finally, in
contrast with usual predictions for crack propagation/healing in infinite
systems, we found a non-monotonic trend of the energy release rates at the
trailing and leading contact edges, which is consistent with the finiteness of
the contact length. All the presented results are strongly supported by
existing experimental evidences.
