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Tribology Letters
Published in: Tribology Letters 3/2022

01-09-2022 | Original Paper

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

Authors: Yang Xu, Xiaobao Li, Daniel M. Mulvihill

Published in: Tribology Letters | Issue 3/2022

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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.
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Metadata
Title
Revisiting the Persson Theory of Elastoplastic Contact: A Simpler Closed-Form Solution and a Rigorous Proof of Boundary Conditions
Authors
Yang Xu
Xiaobao Li
Daniel M. Mulvihill
Publication date
01-09-2022
Publisher
Springer US
Published in
Tribology Letters / Issue 3/2022
Print ISSN: 1023-8883
Electronic ISSN: 1573-2711
DOI
https://doi.org/10.1007/s11249-022-01633-z

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