Adhesive contact problem between thermoelectric material and rigid solid with slightly wavy surface

The thermoelectric effect is a general term for the electrical effects that arise from a temperature difference, as well as the reversible thermal effects induced by electric current, commonly including the Seebeck effect, Peltier effect, and Thomson effect. Thermoelectric devices based on the advantageous thermoelectric effect are increasing used in practical engineering, such as the temperature measurement and thermoelectric power generation. The periodic wavy contact behavior is crucial for the long-term stability and energy conversion efficiency improvement of thermoelectric devices. This paper investigates the two-dimensional periodic Maugis-Dugdale (MD) adhesion contact behavior of thermoelectric half-plane using the integral equation method. The contact problem is transformed into a singular integral equation (SIE) with the Hilbert kernel, in which the size of cohesive zone becomes the key unknown parameter. Through theoretical analysis and numerical calculation, the relationships between normal load, contact zone and adhesion zone under two dimensionless parameters including classical Tabor parameter and the ratio of the surface energy of the grooved surface to the elastic strain energy when the grooved surface is smoothed-out are analyzed, and their curve distributions during loading and unloading are discussed. The results show that rougher surfaces cause more energy loss due to adhesion hysteresis. As the total current and energy flow increase, the normal load necessary to achieve the same contact half-width also rises. This enables us to adjust the surface contact behavior by varying the thermoelectric loads, thereby altering the stress distribution on the contact surface.