Derivations of the stress-strain relations for viscoanelastic media and the heat equation in irreversible thermodynamic with internal variables

Abstract

By using a procedure of classical irreversible thermodynamics with internal variables (CIT-IV), some possible interactions among heat conduction and viscous-anelastic flows for rehological media are studied. By introducing as a tensor ɛ (1) αβ which is contribution to inelastic strain and an vectorial internal variable ξ, which influence thermal and diffusion phenomena, phenomenological equation for these variables are derived. A general vector, J, is introduced which assumes the role of heat flux and it is shown that, in isotropic media, J can be composed of two parts and this allows to obtain a heat equation that generalizes both the Fourier equation and the Maxwell-Cattaneo-Vernotte (M-C-V) equation. A general temperature equation for viscoanelastic media is obtained.