Derivation of Material Constants in Non-Linear Electro-Magneto-Thermo-Elasticity

Abstract

All the investigations on the mechanics and physics of electro-magneto-thermo-elastic materials are based on the set of constitutive equations in which the strain, electric displacement, and magnetic induction and entropy are expressed in terms of the stress, electric field, magnetic field and temperature. A concise formulation of relevant non-linear constitutive relations is presented in this paper. The electro-magneto-thermo-elastic materials show significant interaction among the elastic, electric, magnetic and thermal fields due to the coupled nature of constitutive equations. The thermodynamic Gibbs function of state describes stress, strain, internal energy, electric field, electric displacement, magnetic field, magnetic induction, temperature and entropy. The anisotropic non-linear problem of electro-magneto-thermo-elasticity has been derived on the basis of thermodynamic principle. The Gibbs function is expanded into Taylor series. Material constants have been analyzed from strain, electric displacement, magnetic induction and entropy which are in Gibbs function. In the form of mathematical equations, relationships of material constants have been shown. The derived coefficients (tensor components) of non-linear electro-magneto-thermo-elasticity are presented in tabular forms.