A dynamical theory of polar elastic dielectrics—I

Abstract

Basic axioms of the theory of continuous media are employed to obtain the field equations, jump conditions, and constitutive equations of a polar elastic dielectric subject to large deformations and electromagnetic fields. The theory is dynamical and includes such polar effects as stress moments and electric quadrupole moments. Relativistic effects associated with large material velocities are not incorporated into the theory. Electromechanical interaction forces and their energies are calculated by assuming a distributed Lorentz force on the bound charges within the volume element. The conservation of mass, balance of momenta, conservation of energy, Faraday's Ampere's and Gauss' laws are then postulated in integral form, from which the field equations and jump conditions are obtained systematically. An equation of entropy production is given which is used to derive a nondissipative constitutive theory. Part II will give a properly invariant second order constitutive theory and some illustrative solutions.