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Fractional relaxation processes and fractional rheological models for the description of a class of viscoelastic materials. (English) Zbl 1090.74673

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.

MSC:

74R20 Anelastic fracture and damage
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