### ASA 126th Meeting Denver 1993 October 4-8

## 2pSA1. An overview of fractional-order calculus applied to
viscoelasticity.

**Ronald L. Bagley
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*Structures Div., Wright Lab., Wright--Patterson AFB, OH 45433
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Over the past 80 yr, an initially obscure branch of calculus has gained
some attention as a compact, mathematically convenient description of linear
viscoelasticity. Rieman and Liouville developed the classical definitions of
fractional-order integration and differentiation. These definitions are
fading-memory, linear operators well-suited for describing relaxation,
dispersion, and attenuation effects. Early in this century, several authors
suggested ad hoc fractional-order differentials to describe viscoelastic
effects. Scott Blair first suggested the Rieman and Liouville operators in the
early 1940s. Several investigators have subsequently echoed Scott Blair's
suggestion. More recently, the fractional-order calculus viscoelasticity
formulation has been expanded to include dynamics and finite-element
formulations. Most recently, the formulation has led to the development of the
thermorheologically complex model, a generalization of the thermorheologically
simple material model, and the model has been related to molecular bond energy
decay and fractals. Other recently developed engineering applications of
fractional calculus include corrosion, aeroelasticity, and feedback control.