Dual-phase-lag thermoelastic diffusion analysis of a size-dependent microplate based on modified fractional-order heat conduction model

With the rapid evolution of small-scale devices, the effect of size dependence on elastic deformation becomes more and more obvious. Furthermore, the physical processes usually involve memory and inheritance for some anomalous diffusion that the constitutive relation does not obey the standard gradient rate. Owing to capturing the memory-dependent effect and the size-dependent effect, the existing thermoelastic diffusion theories cannot be applicable. To further refine the thermoelastic diffusion model for micro/nano structures, a refined nonlocal thermoelastic diffusion model is developed by combining the fractional-order dual-phase-lag (DPL) heat conduction model and fractional-order diffusion model in this paper. In addition, the Tempered-Caputo (TC) definition is an extension of the Caputo definition without the fractional derivative of the singular kernel, which is adopted for the first time to reflect the memory-dependent effects of heat conduction and stress-strain relationship. Then, this new model is applied to investigating the transient response of an elastic microplate subjected to a sinusoidal thermal loading. The corresponding governing equations are formulated and solved by the Laplace transform method and its numerical inversion. In calculation, the influences of the fractional-order parameter, the tempered parameter and the nonlocal parameter on the variations of the considered quantities are presented and discussed in detail. It is expected to provide new insights into thermoelastic diffusion behaviors of structures at the micro/nanoscale.