A Multiphysics Theory for the Static Contact of Deformable Conductors With Fractal Rough Surfaces

In this paper, we present a multifield and multiscale theory leading to derivations of electric and thermal conductivities for the interface between two rough surfaces in contact, activated by mechanical load and electric current pulses. At the macroscale, the proposed approach involves multifield coupling of conduction and induction currents, with heat conduction induced by joule heating. The structural mechanics of the conducting materials are also considered. At the mesoscale and microscale, the theory contains a Weierstrass-Mandelbrot description of the rough contact surface profilometry and an asperity-based comprehensive model, respectively. They are both combined to derive homogenized macroscale properties for the interface boundary. The mechanical pressure and the repulsion effect from electric current through the microcontacts are accounted for as well. The results of the numerical analysis illustrate the dependence of the derived properties on the surface characteristics, external load, and electric current. Finally, the entire framework is applied to an actual conductor configuration of hollow cylinders under compression and a high current pulse to demonstrate the feasibility of the entire approach. In addition to providing typical simulation results for all selected fields present during the experiment, we also provide a comparison between the experimentally acquired resistance and the numerically derived resistance to validate the contact theory.