Mechanics of Non-Limiting Equilibrium at Friction

The relevance of studying the highly nonlinear processes of contact interaction between deformable bodies under conditions of non-limit equilibrium during the transition from a state of rest to sliding is demonstrated. A brief review of the results from studies on the phenomenon of pre-sliding displacement is provided. From the perspective of contact mechanics, the peculiarities of theoretical analysis of stress-strain state and wear under compression and compression with shear are discussed. An efficient method for solving the corresponding contact problems, based on the theory of variational inequalities and boundary element discretization of the contact region, is presented.

It is concluded that considering frictional contact as an inhomogeneous surface region consisting of slip zones and stick ones, where tangential displacements are zero, has undoubted fundamental importance for the tribology and mechanics of deformable solids. This is expressed in the correct resolution of the wellknown Painlevé paradox, the mechanical and mathematical interpretation of phenomena of limit equilibrium at friction and in calculated predicting of new effects of contact interaction between bodies made of metamaterials with special (programmable) deformation properties.

The practical significance of this research consists in the possibility of computer-aided design optimization of friction gears and conditionally fixed connections; refining the results obtained during mechanical testing of materials; improving technological methods of material forming (forging, rolling, stamping, and pressing); as well as predicting geomechanical (seismic) events, which are characterized by a state of limit equilibrium in friction.

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