Applications of Fractional Calculus to the Theory of Viscoelasticity

Autor:	R. C. Koeller
Rok vydání:	1984
Předmět:	Mechanics of Materials Mechanical Engineering Mathematical analysis Constitutive equation Relaxation (physics) Condensed Matter Physics Integral equation Viscoelasticity Mathematical physics Fractional calculus Mathematics
Zdroj:	Journal of Applied Mechanics. 51:299-307
ISSN:	1528-9036 0021-8936
DOI:	10.1115/1.3167616
Popis:	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.
Databáze:	OpenAIRE
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