New insights on microscale transient thermoelastic responses for metals with electron-lattice coupling mechanism

Abstract

Microscale transient thermoelastic responses are becoming significantly important with the rapid developments and wide applications of MEMS/NEMS. However, thermal transport and elastic deformation at such scale can't be well described by classical Fourier's law and elastic theory. In this work, theoretical derivation of gradient-type thermoelasticity with electron-lattice coupling mechanism for micro scale metals is systematically given with the aids of generalized thermodynamics and electron-lattice heat conductive model. Numerically, the present model is applied to study the microscale thermoelastic behaviors of a slim strip subjected to thermal shock. For such transient issue, Laplace transform method is adopted, and the analytical solutions are firstly obtained in the Laplace domain, then transient thermoelastic responses for time domain are gotten by numerical inverse Laplace transform method. The results demonstrate that the present model predicts larger responses than that from classical thermoelasticity, such as: higher temperature, larger stress, and bigger heat affected region. Meanwhile, parametric studies are conducted to evaluate the influence of stress gradient parameter, heat flux gradient parameter, and relaxation times on the transient responses, from which a simplified version of microscale thermoelasticity is finally recommended.