Mechanical response and simulation for constitutive equations with distributed order derivatives

被引：7

作者：

Duan J.-S. ^{[1
]}

Chen Y. ^{[2
]}

机构：

[1] School of Sciences, Shanghai Institute of Technology, 100 Haiquan Road, Fengxian District, Shanghai

[2] MESA Lab, University of California, 5200 North Lake Road, Merced, CA

来源：

International Journal of Modeling, Simulation, and Scientific Computing | 2017年 / 8卷 / 04期

关键词：

constitutive equation; distributed order derivative; Fractional calculus; response;

D O I：

10.1142/S1793962317500404

中图分类号：

学科分类号：

摘要：

Mechanical response and simulation for constitutive equation with distributed order derivatives were considered. We investigated the creep compliance, creep recovery, relaxation modulus, stress-strain behavior under harmonic deformation for each case of two constitutive equations. We express these responses and results as easily computable forms and simulate them by using MATHEMATICA 8. The results involve the exponential integral function, convergent improper integrals on the infinite interval (0, +∞) and the numerical integral method for the convolution integral. For both equations, stress responses to harmonic deformation display hysteresis phenomena and energy dissipation. The two constitutive equations characterize viscoelastic models of fluid-like and solid-like, respectively. © 2017 World Scientific Publishing Company.

引用

共 31 条

[1]

Scott-Blair G.W., Analytical and integrative aspects of the stress-strain-time problem, J. Sci. Instrum., 21, pp. 80-84, (1944)

[2]

Scott-Blair G.W., Survey of General and Applied Rheology, (1949)

[3]

Gerasimov A.N., A generalization of linear laws of deformation and its application to inner friction problems, Prikl. Mat. Mekh., 12, pp. 251-259, (1948)

[4]

Caputo M., Mainardi F., Linear models of dissipation in anelastic solids, Riv. Nuovo Cimento, 1, pp. 161-198, (1971)

[5]

Koeller R.C., Applications of fractional calculus to the theory of viscoelasticity, J. Appl. Mech., 51, pp. 299-307, (1984)

[6]

Podlubny I., Fractional Differential Equations, (1999)

[7]

Mainardi F., Fractional Calculus and Waves in Linear Viscoelasticity, (2010)

[8]

Mainardi F., Spada G., Creep, relaxation and viscosity properties for basic fractional models in rheology, Eur. Phys. J. Spec. Top., 193, pp. 133-160, (2011)

[9]

Chen Y., Moore K.L., Analytical stability bound for a class of delayed fractional-Order dynamic systems, Nonlinear Dyn., 29, pp. 191-200, (2002)

[10]

Monje C.A., Chen Y.Q., Vinagre B.M., Xue D., Feliu V., Fractional-Order Systems and Controls, Fundamentals and Applications, (2010)

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