Nonlinear Constitutive Equations for Electromagnetic Crystalline Solids

In this chapter we tabulate the elements of the integrity basis which are invariant under the magnetic symmetry group of the electromagnetic crystalline solids. For the sake of simplicity, the electromagnetic solids considered here are assumed to have the constitutive equations 7.1$$ W = W\left( {{E_{KL}},{P_K},{M_k},\theta } \right) $$ for the internal energy. We have similar expressions for the entropy, the electric field, the magnetic induction, the heat flux, and the stress tensor. The arguments E _KL , P _K , M _K , and θ appearing in (7.1) are, respectively, the material description of the strain tensor (a true, symmetric, and i-tensor), the polarization (a polar and time-symmetric vector), the magnetization (an axial, time-asymmetric vector), and the temperature (a true time-symmetric scalar). The dependent quantities such as the entropy, the electric field, the magnetic induction, and the stress tensor are derived from the internal energy, W, since these materials are conservative (cf. eq. (1.40)).