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Modelling and Simulation in Engineering
Volume 2011 (2011), Article ID 561828, 11 pages
Research Article

A Finite Element-Based Elastic-Plastic Model for the Contact of Rough Surfaces

Department of Mechanical Engineering and Energy Processes, Southern Illinois University Carbondale, Carbondale, Il 62901, USA

Received 24 March 2011; Revised 18 June 2011; Accepted 20 June 2011

Academic Editor: Xiaosheng Gao

Copyright © 2011 Ali Sepehri and Kambiz Farhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Three-dimensional elastic-plastic contact of two nominally flat rough surfaces is considered. Equations governing the shoulder-shoulder contact of asperities are derived based on the asperity constitutive relations from a finite element model of the elastic-plastic interaction proposed by Kogut and Etsion (2002), in which asperity scale constitutive relations are derived using piecewise approximate functions. An analytical fusion technique is developed to combine the piecewise asperity level constitutive relations. Shoulder-shoulder asperity contact yields a slanted contact force consisting of two components, one in the normal direction and a half-plane tangential component. Statistical summation of the asperity level contact force components and asperity level contact area results in the total contact force and total contact area formulae between two rough surfaces. Approximate equations are developed in closed form for contact force components and contact area.