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Journal of Elasticity

, Volume 68, Issue 1–3, pp 167–176 | Cite as

A Molecular-Statistical Basis for the Gent Constitutive Model of Rubber Elasticity

  • Cornelius O. Horgan
  • Giuseppe Saccomandi
Article

Abstract

Molecular constitutive models for rubber based on non-Gaussian statistics generally involve the inverse Langevin function. Such models are widely used since they successfully capture the typical strain-hardening at large strains. Limiting chain extensibility constitutive models have also been developed on using phenomenological continuum mechanics approaches. One such model, the Gent model for incompressible isotropic hyperelastic materials, is particularly simple. The strain-energy density in the Gent model depends only on the first invariant I 1 of the Cauchy–Green strain tensor, is a simple logarithmic function of I 1 and involves just two material parameters, the shear modulus μ and a parameter J m which measures a limiting value for I 1−3 reflecting limiting chain extensibility. In this note, we show that the Gent phenomenological model is a very accurate approximation to a molecular based stretch averaged full-network model involving the inverse Langevin function. It is shown that the Gent model is closely related to that obtained by using a Padè approximant for this function. The constants μ and J m in the Gent model are given in terms of microscopic properties. Since the Gent model is remarkably simple, and since analytic closed-form solutions to several benchmark boundary-value problems have been obtained recently on using this model, it is thus an attractive alternative to the comparatively complicated molecular models for incompressible rubber involving the inverse Langevin function.

Gent constitutive model strain hardening phenomena incompressible rubber 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Cornelius O. Horgan
    • 1
  • Giuseppe Saccomandi
    • 2
  1. 1.Department of Civil EngineeringUniversity of VirginiaCharlottesvilleU.S.A.
  2. 2.Sezione di Ingegneria Industriale, Dipartimento di Ingegneria dell'InnovazioneUniversità degli Studi di LecceLecceItaly

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