Closed‐Form Equations for Contact Force and Moment in Elastic Contact of Rough Surfaces

Abstract

It is reasonable to expect that, when two nominally flat rough surfaces are brought into contact by an applied resultant force, they must support, in addition to the compressive load, an induced moment. The existence of a net applied moment would imply noneven distribution of contact force so that there are more asperities in contact over one region of the nominal area. In this paper, we consider the contact between two rectangular rough surfaces that provide normal and tangential contact force as well as contact moment to counteract the net moment imposed by the applied forces. The surfaces are permitted to develop slight angular misalignment, and thereby contact moment is derived. Through this scheme, it is possible to also define elastic contribution to friction since the half‐plane tangential contact force on one side of an asperity is no longer balanced by the half‐plane tangential force component on the opposite side. The elastic friction force, however, is shown to be of a much smaller order than the contact normal force. Approximate closed‐form equations are found for contact force and moment for the contact of rough surfaces.