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.

Interaction between a thin viscoelastic layer and a rigid cylinder whose contacting end surface is nominally flat but has a microrelief is studied. The microrelief is modeled by a periodic system of axisymmetric indenters. Analytical expressions for the depth of indentation and the real contact area are obtained using an approach based on consideration of micro- and macroscale levels. The effect of the surface microgeometry of the punch and mechanical properties of the layer on the time dependences of the indentation depth and the real contact area is investigated.

The paper presents a two-scales 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 model of indentation of a spherical punch with a rough surface into a thin elastic layer lying on an elastic half-space has been developed. A numerical-analytical solution is suggested based on the two-scales approach. At macroscale, the integral equation of the second kind is reduced to calculate the nominal contact characteristics, taking into account the surface layer thickness and its mechanical characteristics, as well as additional compliance due to surface roughness calculated from the microscale analysis. The influence of the punch roughness and the surface layer mechanical and geometrical characteristics on the nominal contact pressure distribution, on the nominal contact area and the indentation depth, as well as on the real contact area and pressures at the individual contact spots, is analyzed. The developed contact model can be used to analyze the indentation of the punch into the layered elastic base, taking into account the roughness of the punch surface, and can also be used to give a complete analysis of the roughness effect on the contact process at both scale levels. The results can be used to control the indentation of the rough-coated bodies.

Управление внедрением индентора в вязкоупругую ткань с использованием пьезоэлектрического привода