ABSTRACT
This chapter focuses on the static situation and summarizes the equilibrium equations for a solid material capable of large electroelastic deformations. It summarizes the basic electrical and mechanical balance laws and specializes Maxwell's equation for time independent electric fields following the formulation of A. Dorfmann & Ray W. Ogden. The chapter examines constitutive law for an electroelastic material based on the existence of a free energy function. It provides explicit expressions for the total stress tensor and the electric polarization vector in Eulerian and Lagrangian forms for both compressible and incompressible materials. The chapter considers an infinitely long circular cylindrical tube subjected to azimuthal shear and illustrates the change in the mechanical properties for the special case of an applied radial electric field. It examines the equations for a theory of nonlinear electroelasticity and applied them to the problem of a circular cylindrical tube subjected to azimuthal deformation in the presence of a radial electric field.
