A new nonlinear constitutive theory for conducting magnetothermoelastic solids

Abstract

A new nonlinear theory of constitutive equations for electrically and thermally conducting magnetothermoelastic (MTE) solids is developed. In the theory, the electric current and heat flux vectors are also considered to be independent variables in the argument of each constitutive function. It is shown that the modified Helmholtz free energy (MH FE) density, which is a thermodynamical potential for the specific entropy, the magnetization and the stress tensor, does no longer appear as a function of the temperature, the magnetic field and the strain tensor, but it also depends upon the electric current and heat flux vectors. Furthermore, referring to the mentioned constitutive equations, the Gibbs equation is also generalized. In order to expose the constitutive theory developed here, an appropriate polynomial expression of the MH FE density for the anisotropic materials is proposed, and, exploiting the method of the theory of invariants, its exact expression is also determined. With the use of these two expressions, a set of rather general nonlinear constitutive equations, which governs a lot of magnetoelastothermo-electrical (MET-E) effects, is then obtained explicitly. It is interesting to notice that each of the constitutive equations mentioned above has a pseudo (ir) reversible part in vicinities of the new equilibrium state, namely the thermo-electrical equilibrium (T-EE) state. According to the deductive scheme, the generalized constitutive equations and the Gibbs equation in the present work are finally discussed for special materials, and/or vanishing some of the fields. The resulting expressions are, as they should be, in full mutual agreement with the established theories on the same subject.