It is shown that the theory of a fundamental paper of Chadwick and Powdrill on singular surfaces, propagating in a linear thermoelastic body which is stress-free, homogeneous, and isotropic, also holds when the medium is subjected to hydrostatic initial stress provided the two characteristic speeds are suitably changed. The result is obtained by using Biot’s linearization of the constitutive law for the stres

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

We find restrictions on the relaxation functions of thermo-electro-viscoelastic materials. This is achieved within an extension of the Green-Naghdi theory for thermoelasticity, which uses the energy equation to exploit constitutive equations. These restrictions extend the results previously found for thermoviscoelastic materials and for the classical infinitesimal theory of viscoelasticity.KEYWORDS viscoelasticity; thermo-electro-viscoelasticity; relaxation functions; thermodynamic restrictions; restrictions of relaxation functions; Green-Naghdi continuum thermodynamics. Definition 4.1 A dynamic process ( 7) is said to be admissible in B if it is compatible with the constitutive relations (17)-( 19) at each material point X of B and at all times t.

Contents 1 Introduction 1 2 Balance equations 2 3 Constitutive assumptions and restrictions 7 4 Transversely isotropic bodies 13 5 Well-posedness 19 6 Conclusion 23

The Green-Naghdi theoretical approach for thermoelasticity is extended here to thermo-electro-mechanical simple materials with fading memory that are electrically polarizable. Accordingly, the restrictions on the constitutive equations are obtained by exploiting an energy equality rather than an entropy inequality.