Fitting hyperelastic models to experimental data

Ogden, R.W. , Saccomandi, G. and Sgura, I. (2004) Fitting hyperelastic models to experimental data. Computational Mechanics, 34(6), pp. 484-502. (doi: 10.1007/s00466-004-0593-y)

Abstract

This paper is concerned with determining material parameters in incompressible isotropic elastic strain–energy functions on the basis of a non-linear least squares optimization method by fitting data from the classical experiments of Treloar and Jones and Treloar on natural rubber. We consider three separate forms of strain-energy function, based respectively on use of the principal stretches, the usual principal invariants of the Cauchy-Green deformation tensor and a certain set of lsquoorthogonalrsquo invariants of the logarithmic strain tensor. We highlight, in particular, (a) the relative errors generated in the fitting process and (b) the occurrence of multiple sets of optimal material parameters for the same data sets. This multiplicity can lead to very different numerical solutions for a given boundary-value problem, and this is illustrated for a simple example.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Ogden, Professor Raymond
• Authors: Ogden, R.W., Saccomandi, G., and Sgura, I.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Computational Mechanics
• ISSN: 0178-7675
• ISSN (Online): 1432-0924