Power law rheology of generalised Maxwell and Kelvin-Voigt models

Abstract

We analyse the rheological behaviour of the generalised Maxwell and Kelvin-Voigt models with a power law spectrum of relaxation or retardation times, $\mathcal{H}\sim 1/{\tau }^{\alpha }$ or $\mathcal{L}\sim {\tau }^{\alpha }$, respectively. When $0<\alpha <1$, both models have the same weak power law behaviour, which occur in a variety of soft materials, including living cells. Beyond this region, for other values of $\alpha$, the two models have different and distinctive rheological behaviours, converging continuously to the 1-element Maxwell and Kelvin-Voigt models, respectively, for $\alpha <-1$ or $\alpha >2$.

6 pages, 3 figures

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