Contact mechanics and friction of elastic solids on hard and rough substrates

Contact mechanics and friction are topics of huge importance with many applications in Nature andtec hnology. They are closely interconnected, so that understanding friction requires a deep insight into the contact formation between two solids. During university studies, students learn very early that the sliding friction force ?f is proportional to the normal force ?N and independent of the relative sliding velocity, ?f = ??N. The constant of proportionality ?, the coefficient of friction, depends on several parameters, such as the material combination, temperature and surface roughness. Thus one may think that friction is a simple andw ell understood subject. It is, in fact, one of the oldest topics in physics, and a vast amount of work has been investedin order to gain insight into contact mechanics andfriction. Despite all the theoretical and experimental effort, neither topic is well understood. The importance of contact mechanics andfriction cannot be overestimated, as they affect our every day life in countless situations. The reader of this manuscript, for example, wouldb e unable to turn to the next page or walk to the coffee machine in the absence of friction. The complex nature of friction results from its extreme surface sensitivity; a single monolayer of interface atoms or molecules can change the friction by an order of magnitude (or more). In addition, friction usually depends on many decades in length scales, which can be illustrated by two examples. On the nanometer scale, the coefficient of friction between two clean diamond surfaces in ultrahigh vacuum is typically of order 1 or more, because of the strong interaction between the surface dangling bonds. If these bonds are saturated with a hydrogen monolayer, the coefficient of friction decreases rapidly to ≈ 0.05. This shows that even a nanometer thick boundary layer can influence the friction greatly. On the other hand, energy losses due to tidal forces cause the rotation of the earth to slow by the order of 1.6 ⋅ 10−7 seconds per year. This is the reason why during the Cambrian age, approximately 500 Million years ago, the day had only about 21 hours. How to account for all the relevant length scales remains an important and open problem in physics