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

Abstract

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

On adaptive thermo-electro-elasticity within a Green–Naghdi type II or III theory

“…In this section we introduce the balance equations for mass, momentum, energy and entropy following the definitions from [10] and [13]. We apply these equations to the porous matrix B without perfusant.…”

“…Extending the approach from [10], [13] and [27], we consider that the porous matrix structure satisfies the following balance of momentum Extending the approach from [10], [13] and [27], we assume that the porous matrix structure satisfies the following balance of energy…”

“…By considering that we have enough regularity, our integral forms of the balance laws of mass, linear momentum, moment of momentum, entropy and energy, i.e. equations (9), (15), (17), (16), (13) and (14) lead to the system…”

“…Moreover, there exist other models for describing bodies with porosity, see [9], [23]. A detailed account of different models for heat conduction is given in [13]. Examples of applications of transversely isotropic bodies are given for example in [12].…”

“…We follow the Green-Naghdi approach to thermodynamics that uses the concept of thermal displacement and an entropy equality instead of an entropy inequality. Following [10] and [13], we study the bone remodeling process in the context of thermo-electro-elasticity and introduce new balance laws of momentum, energy and entropy. Then we derive the local balance laws, the constitutive assumptions, the constitutive restrictions and finally focus on the case of transversely isotropic bodies.…”