A new nonlinear constitutive theory of electric and heat conductions for magnetoelastothermo-electrical anisotropic solids (Q1068571)

In this paper, a new thermodynamic theory of nonlinear constitutive equations for electric and heat conductions is presented. The theory is based on the new physico-mathematical model of conducting magnetothermoelastic solids exposed in a previous paper [(*) the author, ibid. 22, 683-705 (1984; Zbl 0558.73090)]. Starting from the results given in (*), here we attempt to examine in some details implications of the conduction inequality. In particular, the response functions for the temporal evolution of the electric current and heat flux vectors are determined and the conducting part of the modified Helmholtz free-energy density in the vicinity of the thermo-electrical equilibrium state is specified. Thus the constitutive equations for conduction obtained in the present paper govern acoupling and bicoupling effects between the electric and thermal fields, certain relaxation phenomena and a lot of magnetoelastothermoelectric effects. In short, the Maxwell-Cattaneo equation of heat conduction and the Newtonian-Ohm equation of electric conduction are generalized for the considered material. Furthermore, it is shown that one may need at most six material tensors (moduli) to describe the aforementioned thermoelectric effects and to specify the conducting free-energy density. Finally, it is shown that some special forms of the constitutive equations obtained in this paper are in full agreement with those in the literature.