ANZIAM J. 46(E) pp.C935--C955, 2005.

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

Saiful A. Husain

R. S. Anderssen
(Received 29 January 2004, revised 29 July 2005)

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).

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Authors

Saiful A. Husain
CMA, Mathematical Sciences Institute, Australian National University, Canberra, ACT 0200 Australia; Department of Mathematics, Faculty of Science, Universiti Brunei Darussalam, Gadong, BE 1410 Brunei. mailto:Saiful@fos.ubd.edu.bn
R. S. Anderssen
CSIRO, Mathematical and Information Sciences, GPO Box 664, Canberra, ACT 2601, Australia. mailto:Bob.Anderssen@csiro.au

Published September 22, 2005. ISSN 1446-8735

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Copyright Austral. Mathematical Soc.; prepared September 22, 2005, from Husa.tex with anziamje.sty (v2.3h)