Thermoelastic Generalization of Isothermal Elastic Constitutive Models for Rubber-Like Materials

Abstract

Abstract Existing thermoelastic constitutive models are not able to predict important thermal properties of rubbers. For example, the modified entropic elasticity theory fails to predict that the temperature coefficient of stress, the energetic contribution to the stress, and the specific heat at constant deformation depend on both deformation and temperature. A class of thermoelastic constitutive equations is proposed that generalizes given isothermal models and predicts the temperature and deformation dependence. The Helmholtz free energy is written as the sum of the isothermal energy function, but with temperature-dependent material moduli, and a function of temperature. Conditions on the Helmholtz energy are given to ensure that three inversion effects which characterize rubber are predicted. As an application, an isotropic, homogeneous, mechanically incompressible thermoelastic constitutive equation is generalized from the isothermal Mooney-Rivlin model. The three uniaxial thermal inversion effects are successfully reproduced by this model.