Size-dependent generalized thermoelasticity using Eringen's nonlocal model

TLDR: In this article, the memory dependence of heat conduction is considered using Caputo fractional derivative and m emory d ependent d erivative (MDD) to simulate transient thermo-elastic responses of the nanostructure subjected to a sudden thermal loading.

Abstract: Ultrafast lasers, even the novel laser burst technology, have been widely using in numerous applications, especially in micro-machining. The mechanism of ultrafast laser and matter interaction, such as: heat transfer, deformation of nanostructure, has caught numerous theoretical and experimental research interests. However, in such cases the classical models of thermo-elasticity may be challenged to give accurate responses: firstly, Fourier's law of heat conduction law may break down under the high heat flux and low temperature conditions; secondly, classical elasticity may fail as the external characteristic length (or time) approaches to the internal characteristic length (or time). In this work, to simulate transient thermo-elastic responses of the nanostructure subjected to a sudden thermal loading, classical thermo-elastic models are extended in two aspects: in mechanical sense, Eringen's nonlocal elasticity (differential constitutive relations) is employed to depict the size-dependence; while the memory dependence of heat conduction is considered using Caputo fractional derivative and m emory d ependent d erivative (MDD). In a separated section, the concept of Nonlocal operator and Memory dependent operator are proposed by revisiting Eringen's integral-type nonlocal theory, and comparing fractional calculus, MDD, and a newly reported “Most nature fractional derivative and integral”. In the numerical part, a thermo-elastic medium subjected to a sudden heating at one end is considered, and an analytical technique based on Laplace transform is adopted. While the inverse Laplace transform is numerically implemented by using an efficient and pragmatic algorithm ‘NILT’. Numerical results, i.e., temperature vs. position, displacement vs. position and stress vs. position, are shown graphically, and the influences of nonlocal scale parameter on them are also evaluated. It is concluded that nonlocal scale parameter's effect on the deformation and stress are significant, which is excessively important is determining material's failure when subjected to ultrafast laser like heating, although its effect on the temperature is negligible.