On the constitutive relations for second sound in thermo-electroelasticity

In papers [1] and[2] of 1982, Coleman, Fabrizio and Owen gave a derivation of implications of the second law of thermodynamics to describe second sound in rigid heat conductors by using a natural extension to anisotropic media of the well-known Cattaneo’s relation. Later, in 1992, ¨Onc¨u-Moodie [3] gave a derivation of the constitutive relations of an elastic heat conductor for which the heat flux and the temperature obey a frame-invariant form of a generalized Cattaneo’s equation. Recently, in 2004, Rybalko [4] has shown that a second-sound wave is accompanied by the appearance of electric induction. Here, we extend the theory [3]: following the standard Coleman-Noll procedure [5], we derive the thermodynamic restrictions on the constitutive relations for an electrically polarizable and finitely deformable heat conducting elastic continuum which interacts with the electric field. The constitutive equations include an evolution equation for the heat flux; the latter and the temperature obey a frame-invariant form of Cattaneo’s equation.