Static interaction of rough surfaces under normal force

Modern mechanical engineering designs (and some others) make more and more demands on the development of mathematical models of units in which friction is present. A condition that significantly complicates the study of the properties of a frictional contact is its discreteness with different geometric parameters of two contacting bodies, as a result of which the contact is formed only between a part of the roughness of the rubbing bodies (base and slide). The geometry of the contacting surfaces can most accurately be described by random functions, however, methods for calculating friction nodes based on random functions are very complicated. This work is the initial stage of building a model of contact interaction of two rough bodies with roughness parameters that are different for the two bodies, but constant for each individual body. In addition, the model of contact interaction is considered with a variable force compressing the contacting bodies, in the absence of an external shear force in the contact plane, and this work allows you to check the accuracy of constructing a model of interaction of friction surfaces with a relatively simple scheme of interaction of these surfaces.