Contact analysis of a rigid punch with a periodic wavy surface and functionally graded thermoelectric materials

The multi-field coupled mechanical behavior at the contact interface of thermoelectric devices is a key scientific issue restricting their service performance and structural reliability, so relevant theoretical investigations possess important engineering and academic significance. This paper addresses the thermo-electro-mechanical coupled contact problem between a rigid periodic wavy surface and functionally graded thermoelectric materials. A singular integral equation with a cotangent kernel is established, in which the kernel function involves an infinite series summation and material gradient parameters, enabling simultaneous characterization of the spatially inhomogeneous distributions of electrical conductivity, shear modulus, and thermal expansion coefficient. The Chebyshev collocation method is adopted to achieve highly accurate numerical solutions, with emphasis on the regulation mechanisms of surface morphology, material gradients, electric current load, and energy flux load on contact stress. Results show that surface period, gradient parameters, and energy flux load can significantly modify the contact stress level and distribution profile. Proper gradient matching and energy flux input can effectively alleviate contact stress and realize active control of the contact state. The multi-field coupled contact model constructed in this work provides direct theoretical support and numerical references for stress optimization and structural design of contact interfaces in thermoelectric devices.