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Research Papers

A Novel Constitutive Formulation for Rubberlike Materials in Thermoelasticity

[+] Author and Article Information
Zhu-Ping Huang

Department of Mechanics,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail address: huangzp@pku.edu.cn

Manuscript received June 27, 2013; final manuscript received August 12, 2013; accepted manuscript posted August 22, 2013; published online October 16, 2013. Editor: Yonggang Huang.

J. Appl. Mech 81(4), 041013 (Oct 16, 2013) (8 pages) Paper No: JAM-13-1265; doi: 10.1115/1.4025272 History: Received June 27, 2013; Revised August 12, 2013; Accepted August 22, 2013

The objective of this paper is to present a new framework to formulate thermoelastic constitutive relations for initially isotropic rubberlike materials undergoing finite deformations. The strain-energy function for incompressible materials is extended to include the effects of compressibility and temperature changes. The novelty of this framework is that only a few material functions and material parameters to be fitted with the experimental data are required, and these functions and parameters have clear physical meaning. In order to validate the proposed formulation, the Gent–Gent model for incompressible rubbers is chosen as an illustrative example. A new expression of the Helmholtz free energy of rubberlike materials, which takes into account the material compressibility and thermal effect, is then derived. In this generalized Gent–Gent model, only one material function and six material parameters are introduced. It is shown that the generalized Gent–Gent model can be used to predict the stress-strain behavior over the entire range of deformation. Even for incompressible materials, the strain-energy function in this paper is different from that given by Gent himself. The generalized Gent–Gent model can also adequately describe the thermal-mechanical coupling effect, in which thermoelastic inversion phenomena occur.

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References

Figures

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Fig. 1

Comparisons between the nominal stress-stretch behaviors predicted by Eqs. (16) and (17) and the Treloar data in uniaxial tension and equibiaxial tension

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Fig. 2

Reduced stress versus the reciprocal stretch predicted by Eq. (18)

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Fig. 3

Comparison of the volume ratio-pressure relation predicted by Eqs. (20), (21), and (22)

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Fig. 4

Temperature change of a strip of rubber under an adiabatic extension from the unstretched state to extension ratio λ

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