Hencky-type nonlinear material model for thermoelastic, rubber-like materials

Abstract

It is well-known that linear thermoelastic models are unable to predict the thermoelastic inversion effect and related phenomena in rubber-like polymeric materials. This limitation also applies to the logarithmic stretch-based Hencky-type linear models, even though they can be advantageously applied to moderately large deformations due to the exponential relationship between stress and strain variables. This paper presents a slightly modified Hencky-type thermoelastic constitutive model based on the Gibbs free energy, which is considered a function of the Kirchhoff stress tensor and temperature as independent constitutive variables. By introducing temperature dependence into the material parameters of the linear model, modified constitutive equations for stretch and entropy are derived. The capability of the proposed model to predict the thermoelastic inversion phenomenon and structural heating is investigated for uniaxial and equibiaxial tension problems. The results are compared with those obtained using the nonlinear Ogden–Holzapfel thermoelastic model for incompressible rubber-like materials.