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, ${\cal H}\sim 1/\tau^{\alpha}$ or ${\cal L}\sim \tau^\alpha$, 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 $\alpha>2$.