Revisiting the Persson theory of elastoplastic contact: A simpler closed-form solution and a rigorous proof of boundary conditions

TL;DR

This paper simplifies Persson's elastoplastic contact theory by deriving a closed-form solution as a superposition of Gaussians and provides a rigorous proof of the boundary conditions, enhancing theoretical understanding.

Contribution

It introduces a simpler, closed-form solution for Persson's theory and rigorously proves the boundary conditions, improving analytical clarity.

Findings

P(p, ξ) expressed as a superposition of three Gaussians

Rigorous proof of boundary conditions for P(p, ξ)

Simplified analytical form facilitates further studies

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.