A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum

Syed Mustapha, S.M.F.D. and Phillips, T.N. (2000) A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum. Journal of Physics D: Applied Physics, 33 (10). pp. 1219-1229. ISSN 0022-3727, DOI https://doi.org/10.1088/0022-3727/33/10/313.

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Official URL: https://doi.org/10.1088/0022-3727/33/10/313


The relaxation spectrum is an important tool for studying the behaviour of viscoelastic materials. The most popular procedure is to use data from a small-amplitude oscillatory shear experiment to determine the parameters in a multi-mode Maxwell model. However, the discrete relaxation times appear nonlinearly in the mathematical model for the relaxation modulus. The indirect calculation of the relaxation times is an ill-posed problem and its numerical solution is fraught with difficulties. The ill-posedness of the linear regression approach, in which the relaxation times are specified a priori and the minimization is performed with respect to the elastic moduli, is well documented. A nonlinear regression technique is described in this paper in which the minimization is performed with respect to both the discrete relaxation times and the elastic moduli. In this technique the number of discrete modes is increased dynamically and the procedure is terminated when the calculated values of the model parameters are dominated by a measure of their expected values. The sequence of nonlinear least-squares problems, solved using the Marquardt-Levenberg procedure, is shown to be robust and efficient. Numerical calculations on model and experimental data are presented and discussed.

Item Type: Article
Additional Information: Syed Mustapha, S.M.F.D. 1998-2005. Universiti Malaya, Kuala Lumpur, Malaysia.
Uncontrolled Keywords: Discrete relaxation spectra; Dynamic nonlinear regression method; Marquardt-Levenberg method
Subjects: Q Science > QA Mathematics
Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Divisions: Faculty of Computer Science & Information Technology
Depositing User: Ms. Juhaida Abd Rahim
Date Deposited: 01 Sep 2021 05:07
Last Modified: 01 Sep 2021 05:07
URI: http://eprints.um.edu.my/id/eprint/26007

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