  In this paper we investigate the loading and unloading behavior of soft
solids in adhesive contact with randomly rough profiles. The roughness is
assumed to be described by a self-affine fractal on a limited range of
wave-vectors. A spectral method is exploited to generate such randomly rough
surfaces. The results are statistically averaged, and the calculated contact
area and applied load are shown as a function of the penetration, for loading
and unloading conditions. We found that the combination of adhesion forces and
roughness leads to a hysteresis loading-unloading loop. This shows that energy
can be lost simply as a consequence of roughness and van der Waals forces, as
in this case a large number of local energy minima exist and the system may be
trapped in metastable states. We numerically quantify the hysteretic loss and
assess the influence of the surface statistical properties and the energy of
adhesion on the hysteresis process.
