Power law and fractional calculus model of viscoelasticity

Mathematical relationships between the power law model and the fractional calculus model of viscoelastic behavior are developed. It is demonstrated that the two models have mathematically similar relaxation spectra. This similarity is seen to produce an asymptotic equivalence of the models at long relaxation times and correspondingly low frequencies of motion in the lower transition and rubbery regions. The divergent behavior of the models at higher frequencies in the transition and glassy regions is presented. Porposals to take advantage of the similarities between power law and fractional calculus models are discussed