Fractional Calculus Approach to Dynamic Problems of Viscoelastic Materials.

Abstract

This article presents a review on the application of the fractional calculus to viscoelasticity. There are several methods to treat iscoelasticity of viscoelastie materials. One such method is to use the fractional derivative model for describing the onstitutive relation of the materials. The application of the ractional operator in this field, the Riemann-Liouville's fractional operator is emphasized among several definitions of the fractional operator. The survey suggests that the viscoelastic constitutive models neorporating with the fractional calculus have been well established for fairly wide range of viseoelastic materials and the advantages of adopting the fractional calculus in viscoelasticity are that the constitutive relation of some viscoelastic materials can be described accurately by the fractional aleulus model with a few experimental parameters, and that the fractional calculus approach can lead ω well-posed problems even when incorporated into the finite element formulation.