Derivations of the stress-strain relations for anisotropic viscoanelastic media in irreversible thermodynamics with internal variables

In this paper the rheological and heat equations are derived in an anisotropic viscoanelastic media using the method of internal variables in the absence of external forces. Compared with an isotropic viscoanelastic media, where both the deformation and heat propagation are equal in all directions, this is only possible along certain privileged directions in the anisotropic viscoanelastic case. We have derived the tensor equations describing real behaviour according to privileged directions or main axes which depend on phenomenological and state coefficients. The results are of potential interest in material sciences, in material engineering, and in the analysis of biological tissues.