Applications of Fractional Calculus to the Theory of Viscoelasticity

[+] Author and Article Information
R. C. Koeller

Department of Mechanical Engineering, University of Colorado, Denver, Colo. 80202

J. Appl. Mech 51(2), 299-307 (Jun 01, 1984) (9 pages) doi:10.1115/1.3167616 History: Received March 01, 1983; Revised September 01, 1983; Online July 21, 2009


The connection between the fractional calculus and the theory of Abel’s integral equation is shown for materials with memory. Expressions for creep and relaxation functions, in terms of the Mittag-Leffler function that depends on the fractional derivative parameter β, are obtained. These creep and relaxation functions allow for significant creep or relaxation to occur over many decade intervals when the memory parameter, β, is in the range of 0.05–0.35. It is shown that the fractional calculus constitutive equation allows for a continuous transition from the solid state to the fluid state when the memory parameter varies from zero to one.

Copyright © 1984 by ASME
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