Between Continuum and Atomistic Contact Mechanics: Could We Bridge the Gap?

Abstract

Recently various attempts have been made to compare continuum contact mechanics to atomistic simulations. The general conclusion of these studies is that continuum mechanics is not adequate to study nanoscopic interactions. Although the use of continuum mechanics at the nanometre scale has a number of limitations, some of the results obtained at atomic level using atomistic simulations can be explained at the continuum level by modelling the interacting surfaces as idealised rough contacts. This will be explicitly proven in this paper. The interfacial contact pressure distribution is found for a sphere pressed onto an elastically similar half-space whose surface is populated by a uniform array of spherical asperities (here representing individual atoms). Details of the load suffered by asperities in the contact disk, together with the effects of the roughness on the overall tangential compliance and the frictional energy losses, are found using a recently proposed technique [1]. Results obtained at continuum level are then generalised and compared to those reported in the literature at atomic level. It is shown that the use of the rough contact idealisation described here is capable of reconciling continuum mechanics and atomistic simulations by capturing some of the features that cannot be captured by the means of conventional Hertzian theory.