Journal of Elasticity

, Volume 125, Issue 1, pp 63–71 | Cite as

An Invariant-Based Ogden-Type Model for Incompressible Isotropic Hyperelastic Materials

  • M. B. Rubin
  • A. E. Ehret


The Ogden model for an incompressible isotropic hyperelastic material is versatile enough to match complicated data for rubber-like materials at large deformations. However, the tensorial expression for the Cauchy stress in the Ogden model requires determination of the eigenvalues and eigenvectors of the left Cauchy-Green deformation tensor \(\mathbf{B}\). The objective of this paper is to propose an invariant-based Ogden-type model for isotropic incompressible hyperelastic materials. The strain energy function in this new model depends on classical invariants of \(\mathbf{B}\) and the Cauchy stress tensor can be expressed directly in terms of the tensor \(\mathbf{B}\) without need for its spectral form. Examples show that this new Ogden-type model retains the versatility of the original Ogden model in characterizing material response.


Hyperelasticity Invariants Nonlinear Isotropic 

Mathematics Subject Classification

2.030 2.060 2.080 



This research was partially supported by M.B. Rubin’s Gerard Swope Chair in Mechanics. The authors would like to acknowledge constructive comments of reviewers.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering TechnionIsrael Institute of TechnologyHaifaIsrael
  2. 2.ETH ZurichInstitute of Mechanical SystemsZürichSwitzerland
  3. 3.Empa. Swiss Federal Laboratories for Materials Science and TechnologyDübendorfSwitzerland

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