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

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 no...

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Main Authors: Syed Mustapha, S.M.F.D., Phillips, T.N.
Format: Article
Published: IOP Publishing 2000
Subjects:
QA Mathematics
QA75 Electronic computers. Computer science
Online Access:http://eprints.um.edu.my/26007/
https://doi.org/10.1088/0022-3727/33/10/313
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spelling my.um.eprints.260072021-09-01T05:07:53Z http://eprints.um.edu.my/26007/ A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum Syed Mustapha, S.M.F.D. Phillips, T.N. QA Mathematics QA75 Electronic computers. Computer science 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. IOP Publishing 2000 Article PeerReviewed 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 https://doi.org/10.1088/0022-3727/33/10/313 doi:10.1088/0022-3727/33/10/313
institution Universiti Malaya
building UM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaya
content_source UM Research Repository
url_provider http://eprints.um.edu.my/
topic QA Mathematics
QA75 Electronic computers. Computer science
spellingShingle QA Mathematics
QA75 Electronic computers. Computer science
Syed Mustapha, S.M.F.D.
Phillips, T.N.
A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
description 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.
format Article
author Syed Mustapha, S.M.F.D.
Phillips, T.N.
author_facet Syed Mustapha, S.M.F.D.
Phillips, T.N.
author_sort Syed Mustapha, S.M.F.D.
title A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
title_short A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
title_full A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
title_fullStr A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
title_full_unstemmed A dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
title_sort dynamic nonlinear regression method for the determination of the discrete relaxation spectrum
publisher IOP Publishing
publishDate 2000
url http://eprints.um.edu.my/26007/
https://doi.org/10.1088/0022-3727/33/10/313
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score 13.251813

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