Generalized constitutive relationships for viscoelastic materials are suggested in which the customary time derivatives of integer order are replaced by derivatives of fractional order. To this point, the justification for such models has resided in the fact that they are effective in describing the behavior of real materials. In this work, the fractional derivative is shown to arise naturally in the description of certain motions of a Newtonian fluid. We claim this provides some justification for the use of ad hoc relationships which include the fractional derivative. An application of such a constitutive relationship to the prediction of the transient response of a frequency-dependent material is included.
On the Appearance of the Fractional Derivative in the Behavior of Real Materials
P. J. Torvik,
P. J. Torvik
Department of Aeronautics and Astronautics, Air Force Institute of Technology, WPAFB, Ohio 45433
R. L. Bagley
Department of Engineering Mechanics, USAF Academy, Colorado Springs, Col.
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Torvik, P. J., and Bagley, R. L. (June 1, 1984). "On the Appearance of the Fractional Derivative in the Behavior of Real Materials." ASME. J. Appl. Mech. June 1984; 51(2): 294–298. https://doi.org/10.1115/1.3167615
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