  In this paper, we propose a numerical model to describe the adhesive normal
contact between a "rigid" spherical indenter and a viscoelastic rough
substrate. The model accounts for dissipative process under the assumption that
viscoelastic losses are localized at the (micro)-contact lines. Numerical
predictions are then compared with experimental measurements, which show a
strong adhesion hysteresis mostly due to viscous energy dissipation occurring
during pull-off. This hysteresis is satisfactorily described by the contact
model which allows to distinguish the energy loss due to material dissipation
from the adhesion hysteresis due to elastic instability. Our analysis shows
that the pull-off force required to detach the surfaces is strongly influenced
by the detachment rate and the rms roughness amplitude, but it is almost
unaffected by the maximum load from which unloading starts. Moreover, the
increase in the boundary line separating contact and non-contact regions,
observed when moving from smooth to rough contacts, negligibly affects the
viscous dissipation. Such increase is much less significant than the reduction
in contact area, which therefore is the main parameter governing the strong
decrease in the effective surface energy.
