Joule heating analyses in electrically conductive micro/nano-sized structures

Abstract

Joule heating is occurred in electrically conductive materials. In cracked structures with high concentration of electric current at the crack tip vicinity the Joule heating can be extremely high and even a melting of metal can be observed. It is interesting to investigate thermal stresses caused by this local heating. In micro/nano-sized structures the overheating of structures can be very fast and structure can be damaged. However, in these small structures it is observed the size effect for both heat transport and also for the mechanical balance equation. The thermal transport cannot be described by the classical Fourier’s equation in materials with an internal structure. For mechanical problem due to the size effect the strain gradients have to be considered in the constitutive equations. Then, governing equations for both problems are given by partial differential equations with order of derivatives being higher than in classical case. The collocation mixed FEM is developed here for this multi-physical problem. The present computational method is applied to some crack problem to illustrate compressive stresses at the crack tip vicinity, which are leading to the crack closure.