Mechanics of discrete contact

Abstract

An approach based on the method of averaging is proposed to solve the discrete contact problems for bodies with given macro- and microgeometry. It divides the problem analysis into two scales of sizes. In macroscale the nominal (continuous) contact region is considered, and the integral equation to determine the nominal contact pressure is reduced. This equation includes the additional displacement function which depends on the nominal contact pressure and the microgeometry parameters at the fixed point of the nominal contact region. This function can be determined from the consideration of the discrete contact problem in the microscale for the particular models of surface microgeometry. The periodic contact problem for an elastic half-space has been solved to find the additional displacement function taken into account the interaction between contact spots. The analysis of the system of equations obtained for the periodic problem makes it possible to state the principle of localization which is used to solve the problems in micro- and in macroscale. The influence of the microgeometry parameters on the real and nominal contact characteristics is analyzed.