Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear, optimize lubrication, and enhance the overall performance and durability of mechanical systems. The sliding friction contact problem between a thermoelectric (TE) half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation. To simplify the problem, we utilize mixed boundary conditions, leading to a set of singular integral equations (SIEs) with the Hilbert kernels. The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field. The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials. Notably, the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress, and ensures that it remains free at the contact edge. Based on the plane strain theory of elasticity, the analysis primarily examines the correlation between the applied load and the effective contact area. The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients. Furthermore, the obtained results indicate that the in-plane stress decreases behind the trailing edge, while it increases ahead of the trailing edge when subjected to TE loads.