Constitutive Equations of Nonlocal Electromagnetic Media

Abstract

The formulation of the constitutive equations of electromagnetic (E-M) elastic solids must employ a special type of Helmholtz free-energy functions and a dissipation functional. To this end, we need to develop constitutive equations in the material frame of reference. Thus, the energy equations and the Clausius-Duhem (C-D) inequality are expressed in a material frame. Employing the additive functional, introduced in Section 3.2, we develop separate constitutive equations for the static and dynamic members of the constitutive-dependent variables. This is done by using the C-D inequality. The dynamic members of the constitutive equations require the introduction of the difference histories of the dependent variables. The resulting constitutive equations are nonlocal both in space and time.