A new analytical model for the flattening of Gaussian rough surfaces

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.