In this article we extend the theory of thermoelasticity devised
by Green and Naghdi to the framework of finite thermoelectroelasticity. 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 ther-
mopiezoelectricity is derived from thermodynamic restrictions by construct-
ing the free energy as a quadratic function of the 11 second-order invariants
of the basic melds. The resulting theory provides a natural extension of the
(linear) Green and Naghdi theory for types II and III rigid heat conductors.
As a particular case, we derive the linear system which rules the processes
depending on the symmetry axis coordinate only
