Simulations of dry friction between rough surfaces and corresponding nonlinear problems at nano and microscales

The work is devoted to modelling of dry sliding friction between contacting surfaces and related problems of contact mechanics. To limit the number of physical phenomena involved, the studies are targeted to systems used in vacuum conditions, hence there is no need to consider environmental parameters, such as humidity or oxidation films. Although friction has been studied over many years, challenges remain for obtaining a comprehensive understanding and a quantitative description of influence of nanometre scale effects on friction at micro/macro levels. Many existing models are critically re-examined using ideas of nanoscience. The studies start from the classic Zhuravlev model well-known as the Greenwood - Williamson model representing rough surfaces as collections of spherical elastic asperities. Contact problems for bodies of various shapes are investigated using the Galin solution along with the Borodich rescaling formulae. The rescaling method is applied to indentation experiments by spherical and nominally sharp punches and then a way to model dry friction following Zhuravlev’s arguments is outlined. New ways for numerical simulations of dry sliding friction are presented assuming the friction force is defined by the total energy dissipated over the sliding distance. Novel hierarchical, multiscale, multilevel structural models for simulation of sliding dry friction are presented. The models reflect the physical mechanisms which are most relevant to dry friction at the specific length scales: the chemical interactions at the atomic scale, the adhesive (van der Waals) interactions at the nanoscale, and the mechanical interlocking of asperities and their coupling at the micro and macroscales. Although the models include some features of known models, the nanotribological interpretation of the features is novel. It is argued that the nano-asperities do not deform plastically due to the so-called Polonsky-Keer effect. The obtained results are in good agreement with the experimental observations found in literature