Current-induced thermal stresses in a metal cylinder

Electromechanical coupling has been widely used to actuate and control micromechanical structures and to produce bulk nanostructured materials from micron and submicron particles. The understanding of the mechanical deformation of a mechanical structure carrying an electric current requires the analyses of both electric and current-induced thermomechanical fields. In this work, we analyze the Joule-heating-induced thermoelastic stresses in a metal cylinder which carries an alternating current. Both Joule heating and mechanical stresses are solved analytically for weak skin effect when electric current density varies in radial direction. The thermal stresses created by the Joule heating are found to be a nonlinear function of the angular frequency of the alternating current. The inclusion of the skin effect and radial variation in electric current density in the analyses shows significant quantitative difference in the stress distribution from the thermomechanical deformation of a metal cylinder which carries a direct current.