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).
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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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