A modified fractional-order thermo-viscoelastic model and its application to a polymer micro-rod heated by a moving heat source

Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memory-dependent effect. Meanwhile, with the miniaturization of devices, the size-dependent effect on elastic deformation is becoming more and more important. To capture the memory-dependent effect and the size-dependent effect, the present study aims at developing a modified fractional-order thermo-viscoelastic coupling model at the micro-scale to account for two fundamentally distinct fractional-order models which govern the memory-dependent features of thermal conduction and stress-strain relation, respectively. Then, the modified theory is used to study the dynamic response of a polymer micro-rod heated by a moving heat source. The governing equations are obtained and solved by the Laplace transform method. In calculation, the effects of the fractional-order parameter, the fractional-order strain parameter, the mechanical relaxation parameter, and the nonlocal parameter on the variations of the considered variables are analyzed and discussed in detail.