Nonlocal thermoelasticity and its application in thermoelastic problem with temperature-dependent thermal conductivity

Thermoelastic analysis at the nanoscale is becoming important due to the miniaturization of the device and wide application of ultrashort lasers, and the classical thermoelastic theory is no longer applicable under extreme environments, i.e. extremely high temperature gradient or heat flux, extremely short action time, and extremely small structure size. The nonlocal thermoelastic model is developed to predict the thermoelastic behavior of nanostructures under extreme environments in this paper. The governing equations with temperature-dependent thermal conductivity are solved by Kirchhoff and Laplace transformation. As a numerical example, the transient thermoelastic responses of a slab with temperature-dependent thermal conductivity are investigated. From numerical results, the effects of nonlocal parameters and the temperature-dependent thermal conductivity are discussed, systematically. The results show that the above parameters have significant effects on the transient thermoelastic responses, which is crucial to predict the thermoelastic response accurately for the design and processing of the nanostructures.