Does roughness make elastic-adhesive contacts dissipative?

In this paper we investigate the adhesive contact between a rubber block and rigid randomly rough profiles, in loading and unloading conditions. The roughness is assumed to be described by a self-affine fractal on a limited range of wave-vectors. We employ a spectral method to generate such randomly rough surfaces with different root mean square roughness values and fractal dimensions. Calculations are performed for each profiles by means of an ad hoc numerical code previously developed by the authors.The calculated data are then statistically averaged, and the contact area, the applied load are shown as a function of the penetration, both for loading and unloading conditions. It is found that the combination of adhesion forces and roughness leads to a hysteresis loading-unloading loop, which might be unexpected for perfectly elastic materials. This result is very interesting as it shows that energy can be lost simply as a consequence of roughness and van der Waals forces. Our calculations enable us to numerically quantify such an energy loss and, in particular, to assess the influence of the surface statistical properties and the energy of adhesion on the hysteresis process.