Conjugated kinetic and kinematic measures for constitutive modeling of the thermoelastic continua

Abstract

In this paper, the energy-type terms such as the stress power, the rate of the heat transferred to the system and the rate of the specific internal energy are presented in the Lagrangian, Eulerian and twopoint descriptions for thermoelastic continua. In order to solve a problem based on the energy viewpoint, the mechanical, thermal and thermo-mechanical tensors conjugate to the Seth-Hill strains, and a general class of Lagrangian, Eulerian and two-point strain tensors are determined. Also, the energy pairs for thermoelastic continua are simplified for special cases of isentropic and isothermal deformation processes as well as the so-called entropic elastic materials (rubber-like materials and elastomers). At the end, a strain energy density function of the Saint Venant-Kirchhoff type in terms of different strain measures and temperature is considered for modeling the thermo-mechanical behavior of the rubber-like materials and elastomers. It is shown that this constitutive modeling can give results which are in good agreement with the experimental data.