Constitutive equations and wave propagation in Green-Naghdi type II and III thermoelectroelasticity

In this paper we extend the theory of thermo-elasticity devised by Green and Naghdi to the framework of finite thermo-electroelasticity. Both isotropic and transversely isotropic bodies are considered and thermodynamic restrictions on their constitutive relations are obtained by virtue of the reduced energy equality. In the second part a linearized theory for transversely isotropic thermo-piezoelectricity is derived from thermodynamic restrictions by constructing the free energy as a quadratic function of the eleven second-order invariants of the basic fields. The resulting theory provides a natural extension of the (linear) Green and Naghdi theory for type II and type III rigid heat conductors. As a particular case, we derive the linear system which rules the processes depending on the symmetry axis coordinate, only.