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Zbl 0613.73034
Bagley, R.L.; Torvik, P.J.
On the fractional calculus model of viscoelastic behavior. (English)
[J] J. Rheol. 30, 133-155 (1986). ISSN 0148-6055

It is considered a mathematical model of the viscoelastic phenomenon employing derivatives of fractional order, which is examined with respect to its consistency with thermodynamic principles. The constraints on the parameters of the model are revealed to ensure that the model predicts a nonnegative rate of energy dissipation and nonnegative internal work. Such analysis is fulfilled for an initially five parameter constitutive relation describing the one-dimensional state of stress. Examination of the sinusoidal response shows in particular that the steady-state response predicts a positive material loss factor at all frequencies. \par Analyzing the relaxation and creep responses the authors make the conclusion that satisfaction of thermodynamic constraints leads to a well behaved mathematical description of the viscoelastic phenomenon and is necessary for proper reflection of these responses. A good correlation with the experimental data is also noted. The authors mention in particular that the considered one-dimensional model, parameters of which are calculated on the basis of experiments by the least squares method, yields specific models which are accurate for several decades of material properties.
[V.Korneev]

MSC 2000:: *74D99 Materials of strain-rate type and history type, etc.
74D05 Linear constitutive equations
74D10 Nonlinear constitutive equations
74A20 Theory of constitutive functions

Keywords: derivatives of fractional order; consistency with thermodynamic principles; nonnegative rate of energy dissipation; nonnegative internal work; initially five parameter constitutive relation; one-dimensional state of stress; sinusoidal response; steady-state response; positive material loss factor

Cited in: Zbl 0619.73068

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