A formulation for electrostatic-mechanical contact and its numerical solution

The progress in advanced technology fields requires more and more sophisticated formulations to consider contact problems properly. This paper is devoted to the development of a new constitutive model for electrostatic–mechanical contacts, based on a micro-macro approach to describe the contact behaviour. The electric-mechanical contact constitutive law is obtained considering the real microscopic shape of the contacting surfaces, the microscopic behaviour of force transmission and current flow. Some thermo-mechanical macroscopic models based on microscopic characterizations have already been developed to compute the normal and tangential contact stiffness and the thermal contact resistance. On the basis of such macroscopic models, a similar model, suitable for the electric-mechanical field, is developed. With reference to the thermal constriction resistance the electric contact resistance is studied, assuming a flux tube around each contacting asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contact element geometry is based on well known theoretical and experimental micro-mechanical laws, suitably adapted for the FEM formulation. The macroscopic stiffness matrix is calculated on the basis of the microscopic laws and it is continuously updated as a function of the changes in the mechanical and electric significant parameters. A consistent linearization of the set of equations is developed to improve the computational speed, within the framework of implicit methods.