When rubber slides on a hard, rough substrate, the surface asperities of the substrate exert oscillating forces on the rubber surface leading to energy ''dissipation'' via the internal friction of the rubber. I present a discussion of how the resulting friction force depends on the nature of the substrate surface roughness and on the sliding velocity. I consider in detail the case when the substrate surface has a self affine fractal structure. I also present a theory for the area of real contact, both for stationary and sliding bodies, with elastic or elastoplastic properties. The theoretical results are in good agreement with experimental observation.

Surface roughness has a huge impact on many important phenomena. The most important property of rough surfaces is the surface roughness power spectrum C(q). We present surface roughness power spectra of many surfaces of practical importance, obtained from the surface height profile measured using optical methods and the atomic force microscope. We show how the power spectrum determines the contact area between two solids. We also present applications to sealing, rubber friction and adhesion for rough surfaces, where the power spectrum enters as an important input.

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When two solids are squeezed together they will in general not make atomic contact everywhere within the nominal (or apparent) contact area. This fact has huge practical implications and must be considered in many technological applications. In this paper I briefly review basic theories of contact mechanics. I consider in detail a recently developed contact mechanics theory. I derive boundary conditions for the stress probability distribution function for elastic, elastoplastic and adhesive contact between solids and present numerical results illustrating some aspects of the theory. I analyze contact problems for very smooth polymer (PMMA) and Pyrex glass surfaces prepared by cooling liquids of glassy materials from above the glass transition temperature. I show that the surface roughness which results from the frozen capillary waves can have a large influence on the contact between the solids. The analysis suggest a new explanation for puzzling experimental results [L. Bureau, T. Baumberger and C. Caroli, arXiv:cond-mat/0510232] about the dependence of the frictional shear stress on the load for contact between a glassy polymer lens and flat substrates. I discuss the possibility of testing the theory using numerical methods, e.g., finite element calculations.