Metzler, Ralf; Nonnenmacher, Theo F. Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. (English) Zbl 1090.74673 Int. J. Plast. 19, No. 7, 941-959 (2003). Summary: Following the modelling of Zener, we establish a connection between the fractional Fokker-Planck equation and the anomalous relaxation dynamics of a class of viscoelastic materials which exhibit scale-free memory. On the basis of fractional relaxation, generalisations of the classical rheological model analogues are introduced, and applications to stress–strain relaxation in filled and unfilled polymeric materials are discussed. A possible generalisation of Reiner’s Deborah number \(\daleth\) is proposed for systems which exhibit a diverging characteristic relaxation time. Cited in 25 Documents MSC: 74R20 Anelastic fracture and damage Keywords:Constitutive behaviour; Fractional relaxation processes; Stress relaxation PDFBibTeX XMLCite \textit{R. Metzler} and \textit{T. F. Nonnenmacher}, Int. J. Plast. 19, No. 7, 941--959 (2003; Zbl 1090.74673) Full Text: DOI