A modified fractional-order thermo-viscoelastic model and its application in thermal-induced nonlocal response analysis of a microscale plate

The relaxation process of viscoelastic materials has the memory-dependent effect, while integer-order thermo-viscoelastic models may be challenged to predict precise thermal-mechanical behaviors in solving transient problems of viscoelastic materials in a heat transfer environment. It is found that the fractional-order viscoelastic models fit well with the experimental data from creep and relaxation tests. Additionally, the size-dependent effect on elastic deformation is becoming an issue of great importance recently due to the development of small-scale devices. To capture the memory-dependent and size-dependent effects, the present work aims to formulate a modified fractional-order thermo-viscoelastic model at small-scale for the first time by simultaneously incorporating the effects of the unified definition of the fractional-order parameter, the unified definition of the fractional-order strain parameter and the nonlocal parameter based on the generalized thermo-viscoelastic theory. Then the dynamic response of a viscoelastic microplate under a thermal shock is studied by using the modified fractional-order thermo-viscoelastic model. The corresponding governing equations are formulated and solved by the Laplace transform and its numerical inversion. In conclusion, the influences of the fractional-order parameters, the fractional-order strain parameters and the nonlocal parameters on the variations of the considered quantities are presented and discussed in detail. The obtained results show that these parameters significantly influence the variations of all the considered quantities.