Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories

Abstract

Ultra-slow relaxation process of polymers has the memory-dependent feature, integer-order thermoviscoelastic models may fail to describe the dynamic behaviors of viscoelastic structures accurately. Additionally, it is noticed that the small-scale effect of elastic deformation and heat conduction in a non-isothermal temperature environment is becoming significant due to the development of micro-devices. To better capture the memory-dependent effect and the small-scale effect of viscoelastic micro-structures in heat transfer environment, as a first attempt, present work focuses on developing a refined fractional Kelvin-Voigt thermoviscoelastic model by incorporating the nonlocal dual-phase-lag (NDPL) heat conduction model and the modified coupled stress theory (MCST). Then, the model is applied to investigating the transient response of a polymer microbeam subjected to a harmonic thermal loading. The governing equations involving the modified parameters are formulated and then solved by Laplace transform method. Some parametric results are demonstrated to display the impacts of the nonlocal thermal parameter, the material length-scale parameter and the fractional-order parameter on the considered physical quantities. The results show that the small-scale effect and the memory-dependent effects strongly depend on the polymer micro-structure characteristics in thermal environment.

Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative

“…Comprehending its inherent stability is crucial in order to forecast the extended-term performance of the nanobeam. In conclusion, a crucial factor in understanding how elastic nanobeams vibrate is the viscous damping coefficient 59 , 60 . For the purpose of designing and optimising nanomechanical systems and devices, it is imperative that their incorporation into mathematical models be used in order to precisely forecast and comprehend the changing behaviour of viscoelastic nanostructures 61 .…”

“…This model is commonly used to represent the viscoelastic behaviour of materials, where both the rate of deformation influences their mechanical properties over time and the duration of applied loads. The modified Young's modulus is expressed as 60 : where is the elastic Young's modulus and is the vicosity or viscous damping coefficient. Substituting Eqs.…”