A New Principle in Contact Mechanics

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Abstract
Two nonrotating elastic half-planes in quasi-static contact without coupling of the normal and tangential surface stresses are analyzed in this paper. It is proved that the tangential traction under constant normal forces and increasing tangential forces is equal to the difference between the actual normal pressure and the pressure for a smaller contact area, multiplied by the coefficient of friction. Every stick area corresponds to a contact area (or a configuration of multiple contact areas) that is smaller than the present contact area. In the same way as the contact area develops with increasing pressure, the stick area recedes with increasing tangential traction. General loading scenarios are solved by superposition of oblique increments under constant angles. As an example, this principle is applied to a rigid surface of the form Ak xk , in contact on 0 ≤ x ≤ a and with a corner at x = 0, indenting an elastic half-plane.

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