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

Xu, Y., Li, X. and Mulvihill, D. M. (2022) Revisiting the Persson theory of elastoplastic contact: a simpler closed-form solution and a rigorous proof of boundary conditions. Tribology Letters, 70(3), 91. (doi: 10.1007/s11249-022-01633-z)

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,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.

• Item Type: Articles
• Additional Information: This work was supported by the Leverhulme Trust through Project Grant “Fundamental mechanical behavior of nano and micro structured interfaces” (RPG-2017-353), the National Natural Science Foundation of China (No. 52105179), the Fundamental Research Funds for the Central Universities of China (No. PA2021KCPY0029) and Jiangsu Key Laboratory of Engineering Mechanics, Southeast University (No. LEM21A03).
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Mulvihill, Dr Daniel

Creator Roles

Mulvihill, D.: Methodology, Writing – review and editing, Funding acquisition

• Authors: Xu, Y., Li, X., and Mulvihill, D. M.
• College/School: College of Science and Engineering > School of Engineering > Systems Power and Energy
• Journal Name: Tribology Letters
• Publisher: Springer
• ISSN: 1023-8883
• ISSN (Online): 1573-2711
• Published Online: 30 July 2022
• Copyright Holders: Copyright © 2022 The Authors
• First Published: First published in Tribology Letters 70(3):91
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
302858		Fundamental Mechanical Behaviour of Nano and Micro Structured Interfaces	Daniel Mulvihill	Leverhulme Trust (LEVERHUL)	RPG-2017-353	ENG - Systems Power & Energy