A memory-dependent thermal-viscoelastic model and its application in heating-induced nonlocal response analysis of a polymer microbeam

Abstract

In order to capture the memory-dependent effect and size-dependent effect, present work aims to develop a novel thermo-viscoelastic nonlocal model in micro-scale for the first time to include the simultaneous effects of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function. Then, the theory is applied to studying the dynamic response of a polymer microbeam heated by a ramp-type heating. In calculation, the influences of the fractional order parameter, the viscous damping coefficient, the time-delay factor and the kernel function on the variations of the considered variables are presented and discussed in detail.

Keywords:

• Memory-dependent derivative
• fractional Kelvin–Voigt model
• size-dependent effect
• polymer microbeam
• thermo-viscoelastic response

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [11972176, 12062011] and the Incubation Programme of Excellent Doctoral Dissertation-Lanzhou University of Technology.