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

• Published in: Applied mathematics and mechanics Vol. 43; no. 4; pp. 507 - 522
• Main Authors: Peng, Wei, Chen, Like, He, Tianhu
• Format: Journal Article
• Language: English
• Published: Shanghai Shanghai University 01.04.2022; Springer Nature B.V; School of Science,Lanzhou University of Technology,Lanzhou 730050,China; Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China%School of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China%Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China
• Edition: English ed.
• Subjects: Applications of Mathematics; Classical Mechanics; Deformation effects; Dynamic response; Elastic deformation; Fluid- and Aerodynamics; Laplace transforms; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Mechanical properties; Miniaturization; Order parameters; Partial Differential Equations; Polymers; Strain; Stress-strain relationships; Thermomechanical properties; Viscoelastic materials; Viscoelasticity; fractional-order strain; moving heat source; 74F05; size-dependent effect; fractional-order thermal conduction; generalized thermo-viscoelasticity; O343.6; fractional-order thermal con-duction
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-022-2835-9

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.