# Mesoscopic Aspects of Solid Friction

The phenomenon of friction is on the one hand useful, for example for walking, which would not be so easy without friction, and on the other hand disturbing, for example in wheel bearings, where it slows down desired motion. Therefore, the origin and effect of friction is under intense research. One main point in this work is the analytic investigation of the coupling between friction force and (torsion) friction torque of a sliding and spinning disk. The local friction force at a contact area element was chosen to be an algebraic function of the local relative velocity with an exponent α > 0. It could be shown, that for α < 1 sliding and torsion friction dynamically reduce each other, while for α > 1 they amplify each other. In case of α = 1 sliding and torsion friction are decoupled. With respect to the velocity ratio of sliding and angular velocity, the final motion mode has been investigated, i.e. whether both motions stop together or whether one motion gets dominant. For α < 1 both motions stop together, while for α > 1 it depends on the initial velocity ratio. The mass distribution and contact area radius, which are encoded in the key parameter C of the corresponding differential equation, are the second important influence on the final motion mode. A “phase diagram” shows for given values C and α the possible final motion modes. The influence of an inhomogenous pressure distribution within the contact area on the coupling was investigated exemplarily for α = 0 with a cylinder as object. In contrast to the disk (homogenous pressure distribution) the cylinder is deflected from its initial sliding direction. In this context the motion of a curling rock on ice is discussed, as it is deflected towards the opposite direction compared to that of the cylinder. Another focal point is the investigation of the role of friction torques (rolling and torsion friction) in the compaction of nano-powders. For this three dimensional contact dynamics simulations with phenomenologically chosen contact laws were performed. With this it could be shown that torsion and rolling friction contribute significantly to the final porosity. Furthermore, these contributions of torsion and rolling friction are independent of each other and can be represented by a sum. In the chapter “Conclusions and Outlook” a brief introduction on recent research of atomic scale torsion friction is presented.

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