On Entropy Flux of Transversely Isotropic Elastic Bodies

Recently (Liu in J. Elast. 90:259-270, 2008) thermodynamic theory of elastic (and viscoelastic) material bodies has been analyzed based on the general entropy inequality. It is proved that for isotropic elastic materials, the results are identical to the classical results based on the Clausius-Duhem inequality (Coleman and Noll in Arch. Ration. Mech. Anal. 13:167-178, 1963), for which one of the basic assumptions is that the entropy flux is defined as the heat flux divided by the absolute temperature. For anisotropic elastic materials in general, this classical entropy flux relation has not been proved in the new thermodynamic theory. In this note, as a supplement of the theory presented in (Liu in J. Elast. 90:259-270, 2008), it will be proved that the classical entropy flux relation need not be valid in general, by considering a transversely isotropic elastic material body.