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Non-linear optimization of the material constants in Ogden's stress-deformation function for incompressinle isotropic elastic materials

Published online by Cambridge University Press:  17 February 2009

E. H. Twizell  and
R. W. Ogden
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Abstract

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In previous papers, three terms have been included in Ogden's stress-deformation function for incompressible isotropic elastic materials. The material constants have been calculated by elementary methods and the resulting fits to sets of experimental data have been moderately good.

The purpose of the present paper is to improve upon established correlation between theory and experiment by means of a systematic optimization procedure for calculating material constants. For purposes of illustration the Levenberg-Marquardt non-linear least squares optimization algorithm is adapted to determine the material constants in Ogden's stress-deformation function.

The use of this algorithm for three-term stress-deformation functions improves somewhat on previous results. Calculations are also carried out in respect of a four-term stress-deformation function and further improvement in the fit is achieved over a large range of deformation.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 4 , April 1983 , pp. 424 - 434
Copyright
Copyright © Australian Mathematical Society 1983

References

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