A new analytical model for the contact of Gaussian rough surfaces

TL;DR

This paper introduces an analytical model for elastic and elastic-plastic Gaussian rough surface contact, accurately predicting contact area and load relationships, validated by finite element simulations, and incorporating plastic deformation effects.

Contribution

The paper presents a novel analytical incremental contact model for Gaussian rough surfaces that accounts for elastic and plastic deformation, validated against finite element results.

Findings

Contact area-load relationship is approximately linear up to 10% contact fraction.

Good agreement between the analytical model and finite element simulations.

Plastic deformation influence characterized by a dimensionless parameter, approaching elastic response as it increases.

Abstract

This paper advances an analytical incremental contact model for the purely elastic or elastic-perfectly plastic Gaussian rough surfaces. The contact is modelled by the accumulation of identical circular contacts with radius given by the total truncated area at varying heights divided by the contact patch number. The contact area-load relationship is derived analytically, showing approximate linearity for the contact fraction up to 10%. Good agreement is found between the new proposed model and the direct finite element simulations. To characterize the influence of plastic deformation, a dimensionless plasticity parameter is introduced as the ratio of yield strain to root mean square gradient of the rough surface. It is demonstrated that the general elastic-plastic contact response would approach to the limit of purely elastic as the plasticity parameter increases.