Interaction of Two Elastic Bodies in the Presence of Periodically Located Gaps Filled with a Real Gas

Abstract

We model contact interaction of two elastic semiinfinite bodies in the presence of a real gas in the interface gaps formed by a periodic array of grooves on the surface of one of the bodies. The state of the gas is described by the van der Waals equation, which enables us to consider the phase transition from the gas into the liquid phase. The posed contact problem is reduced to a singular integral equation with Hilbert kernel for the height of the gap. This equation is transformed into a singular integral equation with Cauchy kernel and is solved analytically. To determine the length of the gap and gas pressure, we derive a system of transcendental equations from the condition of boundedness of the solution of this singular integral equation and from the van der Waals equation. The dependences of the gap length, gas pressure, contact approach, and contact compliance of the bodies on the applied load are analyzed.