Computational Mechanics

, Volume 34, Issue 6, pp 484–502 | Cite as

Fitting hyperelastic models to experimental data

  • R. W. OgdenEmail author
  • G. Saccomandi
  • I. Sgura


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 ‘orthogonal’ 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.


Constitutive laws Elasticity Elastomers Finite deformation Isotropic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of GlasgowGlasgowUK
  2. 2.Dipartimento di Ingegneria dell’InnovazioneSezione di Ingegneria Industriale, Università degli Studi di LecceLecceItaly
  3. 3.Dipartimento di MatematicaUniversità degli Studi di LecceLecceItaly

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