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

Abstract: We present a numerical model for the prediction of the rough contact mechanics of a viscoelastic block, with graded rheology, in steady sliding contact with a randomly rough rigid surface. In particular, we derive the effective surface response of a stepwise or continuously-graded block in the Fourier domain, which is then embedded in a Fourier-based residuals molecular dynamic formulation of the contact mechanics. Finally we discuss on the role of small-scale wavelengths on rubber friction and contact area, and 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 realistic rheology of the confinement is taken into account.