A contact formulation for electrical and mechanical resistance

In this paper a formulation to deal with the Finite Element modelling of coupled electric-mechanical contact resistance is presented. The electrical contact resistance is based on a micro-macro approach, i.e. the contacting surfaces are not considered as perfectly smooth, but are characterised at the microscopic level by the presence of valleys and peaks. Such roughness reduces the real contact area to a very small percentage of the apparent one. The microscopic geometry thus plays a very important role in perturbing any type of field (mechanical, thermal, electrical etc.) in the contact zone. Some macroscopic models, based on microscopic characterizations, have been proposed to describe the normal and tangential contact stiffness and the thermal contact resistance. Within such models, the surface microrugosity of the asperities in contact is taken into account by replacing each surface by a statistically equivalent one. The load-flattening mechanical behaviour of the contacting asperities is modelled by choosing a perfectly plastic constitutive law as well as an elastic one. In this way the mean plane approach is obtained as a function of the applied load variation. The smallness of the real contact area causes a perturbation also of the electric field. The flux lines must concentrate where the asperities are in contact. In analogy with the thermal contact resistance this electrical constriction resistance is studied, supposing a flux tube around each asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contributions, due to each flux tube, are added in parallel to determine the electric resistance of the apparent contact area. The contact constitutive law so obtained, is then consistently linearized, in order to keep the quadratic convergence of the Newton-Raphson iterative scheme