Surface roughness causes contact to occur only at discrete spots called microcontacts. In the deterministic models real area of contact and pressure field are widely evaluated using Flamant and Boussinesq equations for two-dimensional (2D) and three-dimensional (3D), respectively. In this paper, a new 3D geometrical contact approach is developed. It models the roughness by cones and uses the concept of representative strain at each asperity. To discuss the validity of this model, a numerical solution is introduced by using the spectral method and another 3D geometrical approach which models the roughness by spheres. The real area of contact and the pressure field given by these approaches show that the conical model is almost insensitive to the degree of isotropy of the rough surfaces, which is not the case for the spherical model that is only valid for quasi-isotropic surfaces. The comparison between elastic and elastoplastic models reveals that for a surface with a low roughness, the elastic approach is sufficient to model the rough contact. However, for surfaces having a great roughness, the elastoplastic approach is more appropriate to determine the real area of contact and pressure distribution. The results of this study show also that the roughness scale modifies the real contact area and pressure distribution. The surfaces characterized by high frequencies are less resistant in contact and present the lowest real area of contact and the most important mean pressure.

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