Revisiting the Persson Theory of Elastoplastic Contact: A Simpler Closed-Form Solution and a Rigorous Proof of Boundary Conditions

Abstract

Persson’s theory of contact is extensively used in the study of the purely normal interaction between a nominally flat rough surface and a rigid flat. In the literature, Persson’s theory was successfully applied to the elastoplastic contact problem with a scale-independent hardness H. However, it yields a closed-form solution, \(P(p, \xi )\), in terms of an infinite sum of sines. In this study, \(P(p, \xi )\) is found to have a simpler form which is a superposition of three Gaussian functions. A rigorous proof of the boundary condition \(P(p=0, \xi )=P(p=H, \xi ) = 0\) is given based on the new solution.