Finite thermoelasticity with limiting chain extensibility

Rubber-like materials and soft tissues exhibit a significant stiffening or hardening in their stress strain curves at large strains. Considerable progress has been made recently in the phenomenological modeling of this effect within the context of isotropic hyperelasticity. In particular, constitutive models reflecting limiting chain extensibility at the molecular level have been used to accurately capture strain-hardening. Here we generalize such models to isotropic thermoelasticity. We also show that specific non-polynomial strain-energies for both hyperelastic and thermoelastic materials can be obtained on using a modification of a systematic scheme of Rivlin and Signorini. The Rivlin-Signorini method was based on approximation of the strain-energy density function by polynomials whereas here we use the more general class of rational functions to approximate: the material response functions. We then propose a simple generalization to thermoelasticity, of a constitutive model for incompressible hyperelastic materials reflecting limiting chain extensibility due to Gent (Rubber Chem. Technol. 69 (1996) 59-61). For this new thermoelastic constitutive model we investigate the inhomogeneous deformation problem of axial shear, of a circular cylindrical tube. (C) 2003 Elsevier Science Ltd. All rights reserved.