On Entropy Flux of Anisotropic Elastic Bodies

The framework of irreversible thermodynamics is fundamental in development of constitutive models. One of the important aspects of the extended irreversible thermodynamics is the relationship between the entropy flux and the heat flux, especially for phenomena far from equilibrium. In this paper, we demonstrate that the assumption that Lagrange multiplier conjugated to the energy balance equation (in the expression for the second law of thermodynamics) is a function of temperature Λε=Λε(θ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \varLambda^{\varepsilon } = \varLambda^{\varepsilon } (\theta ) $$\end{document} is a sufficient condition to derive the entropy flux–heat flux relation for all isotropic materials as well as for a number of crystal classes including transverse isotropy, orthotropy, triclinic systems and rhombic systems. For all considered crystal classes, the entropy flux–heat flux relation was derived explicitly. Further, we demonstrate that for some crystal classes heat flux is nonzero even when temperature gradient vanishes (as stated by Eringen). The anisotropic functions, with respect to the symmetry groups of the crystal classes, were expressed in terms of isotropic functions. The proposed procedure is very general in the sense that it can be used with nonlinear constitutive relations as demonstrated here. The presented results confirm that the all crystal elastic bodies considered are hyperelastic.