Rough contact mechanics for viscoelastic graded materials: The role of small-scale wavelengths on rubber friction

We discuss on the rough contact mechanics in presence of a graded viscoelastic solid. In particular, we derive the effective surface admittance of a stepwise or continuously-graded half-space, which is then embedded in a Fourier-based residuals molecular dynamics formulation of the contact mechanics. The viscoelastic multilayer theory, which is of general applicability, is then applied to discuss on the role of small-scale wavelengths on polymer friction and contact area. We demonstrate that the rough contact mechanics exhibits effective interface properties which converge to asymptotes upon increase of the small-scale roughness content, when a more realistic rheology of the confinement is taken into account.