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

摘要

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.

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