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Persson's theory of contact is extensively used in the study of the purelynormal interaction between a nominally flat rough surface and a rigid flat. Inthe literature, Persson's theory was successfully applied to the elastoplasticcontact problem with a scale-independent hardness $H$. However, it yields aclosed-form solution, $P(p, \xi)$, in terms of an infinite sum of sines. Inthis study, $P(p, \xi)$ is found to have a simpler form which is asuperposition of three Gaussian functions. A rigorous proof of the boundarycondition $P(p=0, \xi)=P(p=H, \xi) = 0$ is given based on the new solution.

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