Algorithms for the recovery of Kohlrausch parameters from viscoelastic stress-strain data

Abstract

The Boltzmann model of linear viscoelasticity is an appropriate model for materials that simultaneously exhibit viscous and elastic behaviour, such as synthetic and natural polymers. The nature of the viscoelasticity is encapsulated in terms of the structure of its kernel function (the relaxation modulus) G(t). Husain and Anderssen (2005) proposed a procedure for approximating G(t), based on taking moments of the Boltzmann equation with G(t) the sum of Kohlrausch functions. The shortcoming of this proposal is the need to evaluate the moments on the half-interval [0,?). We propose a method which takes the strain-rates to have a polynomial form and G(t) to be a sum of Kohlrausch functions. It yields methods for the direct estimation of the parameters in Kohlrausch models for G(t).