This paper presents a two-scale analytical approach to study the normal contact of deformable bodies, taking into account their surface roughness. This approach makes it possible to evaluate the influence of roughness on both real contact characteristics (microscale) and nominal ones (macroscale). The advantage of the presented approach is demonstrated by solving several contact problems. At microscale, contacts of rigid rough surfaces with elastic and viscoelastic half-spaces are considered based on periodic and probabilistic roughness descriptions. The interaction of asperities is taken into account by the localization method. At macroscale, contacts of punches of various macroshapes, which have rough contact surfaces, and deformable homogeneous and inhomogeneous bases are studied. It is shown that roughness parameters determine the additional compliance of deformable bodies. In turn, the additional compliance function influences the distribution of nominal pressures, as well as the size of the nominal contact area. The presented solutions can be used to control the contact characteristics by selecting a suitable microrelief of the contacting surfaces and to predict the durability of contact pairs based on analysis of internal stresses and wear processes.

The contact of a rigid body with nominally flat rough surface and an elastic half-space is considered. To solve the contact problem, the Greenwood‒Williamson statistical model and the localization principle are used. The developed contact model allows us to investigate the surface approach and the real contact area with taking into account the asperities interaction. It is shown that the mutual influence of asperities changes not only contact characteristics at the macroscale, but also the contact pressure distribution at the microscale. As follows from the results, the inclusion in the contact model of the effect of the mutual influence of asperities is especially significant for studying the real contact area, as well as the contact characteristics at high applied loads. The results calculated according to the proposed approach are in a good agreement with the experimentally observed effects, i.e., the real contact area saturation and the additional compliance exhaustion.