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General Information
    • ISSN: 1793-8198
    • Frequency: Quarterly
    • DOI: 10.18178/IJMMM
    • Editor-in-Chief: Prof. K. M. Gupta, Prof. Ian McAndrew
    • Executive Editor: Ms. Cherry L. Chen
    • Abstracting/Indexing: EI (INSPEC, IET), Chemical Abstracts Services (CAS), Engineering & Technology Digital Library,  ProQuest, Crossref, Ulrich's Periodicals Directory, and Electronic Journals Library .
    • E-mail ijmmm@ejournal.net
Editor-in-chief
Prof. Ian McAndrew
Embry Riddle Aeronautical University, UK.
It is my honor to be the editor-in-chief of IJMMM. I will do my best to help develop this journal better.

IJMMM 2018 Vol.6(3): 191-194 ISSN: 1793-8198
DOI: 10.18178/ijmmm.2018.6.3.374

A Generalized Constitutive Equation with Distributed Order Derivative for Viscoelastic Solid

Lingjie Duan and Junsheng Duan
Abstract—In order to generalize the Kelvin-Voigt model describing viscoelastic solids, we present a constitutive equation with distributed order derivative. Using the Laplace transform and its numerical inverse, we consider the creep compliance, creep recovery, relaxation modulus, and stress response to harmonic deformation. The results show that the constitutive equation indeed characterizes viscoelastic solids and is a generalization of the Kelvin-Voigt model. Meanwhile, we discuss the effect of the modelling parameter on viscoelasticity.

Index Terms—Constitutive equation, distributed order derivative, fractional calculus, response.

L. Duan is with the State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, P.R. China (e-mail: dlj14141144@hotmail.com).
J. Duan is with the School of Sciences, Shanghai Institute of Technology, Shanghai 201418, P.R. China (e-mail: duanjs@sit.edu.cn).

[PDF]

Cite: Lingjie Duan and Junsheng Duan, "A Generalized Constitutive Equation with Distributed Order Derivative for Viscoelastic Solid," International Journal of Materials, Mechanics and Manufacturing vol. 6, no. 3, pp. 191-194, 2018.

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