Thermal stress induced by electric current in the vicinity of an elliptic inclusion in an infinite plate

We consider an elliptic inclusion embedded in an infinite plate subjected to the simultaneous effects of electric current and energy flux at infinity. Using complex variable methods, we analyze the resulting mechanical properties of the composite, in particular around the perimeter of the inclusion. In doing so, we find that thermal stress can exist even in a simply connected region as a result of Joule heating which can therefore be used to preset stress in manufactured devices. In the particular case of the elliptic inclusion, we find that the electric current has the ability to transfer thermal stress to regions of lower temperature thereby improving security and reliability of the corresponding devices.