Dual-phase-lag thermoviscoelastic analysis of a size-dependent microplate based on a fractional-order heat-conduction and strain model.

Integer-order thermoviscoelastic models may fail to give an accurate description of the thermomechanical behavior of viscoelastic materials, which inherently have the memory-dependent feature. Meanwhile, with the miniaturization of devices, the small-scale effect on elastic deformation is becoming increasingly significant. To better describe the memory-dependent effect and the small-scale effect in viscoelastic microstructures, this work focuses on developing a refined nonlocal thermoviscoelastic model by incorporating the fractional-order dual-phase-lag (DPL) heat-conduction model and the fractional-order strain model. Moreover, the Caputo–Fabrizio (CF) definition and the Tempered-Caputo (TC) definition of the fractional derivative without a singular kernel as well as the extension of the Caputo definition are adopted to reflect the memory-dependent effects of the heat conduction and the stress–strain relation for the first time, respectively. Then, this new model is applied to investigate the transient response of a viscoelastic microplate subjected to a sinusoidal thermal loading. The governing equations involving the modified parameters are formulated and then solved by the Laplace-transform method. Some parametric results are demonstrated to display the impacts of the fractional-order parameter, the fractional-order strain parameter and the nonlocal parameter on the considered physical quantities. The results show that the nonlocal effect and the memory-dependent effect strongly depend on the viscoelastic microstructure characteristics in a thermal environment. [ABSTRACT FROM AUTHOR]