A physical basis for fractional derivatives in constitutive equations

摘要

In good coincidence with experimental data the damping properties of viscoelastic media can be described by fractional derivatives. We present a model, which under certain assumptions on the interactions between macromolecules leads to a macroscopic stress strain relation with fractional derivatives in the damping term. For this purpose we use the Kubo formula of nonequilibrium thermodynamics. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.