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

作　　者：Wei PENG Like CHEN Tianhu HE 

机构地区：[1]Key Laboratory of Disaster Prevention and Mitigation in Civil Engineering of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China [2]School of Civil Engineering and Mechanics,Lanzhou University,Lanzhou 730000,China [3]School of Science,Lanzhou University of Technology,Lanzhou 730050,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2022年第4期507-522,共16页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11972176 and12062011)。

摘　　要：Classical thermo-viscoelastic models may be challenged to predict the precise thermo-mechanical behavior of viscoelastic materials without considering the memorydependent 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 microscale 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.

关 键 词：size-dependent effect fractional-order strain fractional-order thermal conduction generalized thermo-viscoelasticity moving heat source 

分 类 号：O343.6[理学—固体力学]