Nonlinear laws of dry friction in contact problems of linear theory of elasticity

A problem of elastic body deformation with conditions of dry friction imposed at the boundary is considered. Various friction laws are studied, including linear one-parameter and nonlinear two-parameter laws. A general view of a nonlinear function with two constants is suggested, which determines the friction force as a function of normal pressure. The problem of elastic plate compression by rough infinite plates for a variety of friction conditions on the contact surfaces is solved. The plate equations are employed, which make it possible to specify arbitrary conditions on the front faces without reducing the order of differential equations. The unknown boundary of ideal contact zones and sliding zones is determined. Solutions obtained by using various friction conditions on the contact surfaces are compared.