A Novel Constitutive Formulation for Rubberlike Materials in Thermoelasticity

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.