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

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, $P(p, ξ)$, in terms of an infinite sum of sines. In this study, $P(p, ξ)$ is found to have a simpler form which is a superposition of three Gaussian functions. A rigorous proof of the boundary condition $P(p=0, ξ)=P(p=H, ξ) = 0$ is given based on the new solution.