A constitutive equation for non-linear electro-active solids

Electro-active solids are solids that are either infused with electrorheolo gical fluids or embedded with electrically conducting particles, the body a s a whole however conducting negligible current. In this paper, we provide a mathematical framework, within the context of continuum mechanics, for th e study of electro-active solids. The theory assumes that the body can be c onsidered as a continuum, in the sense of homogenization, which is isotropi c, incompressible, elastic and is capable of responding to an electric fiel d. Appealing to standard techniques in continuum mechanics, we obtain a con stitutive relation for the stresses in terms of the deformation and electri c field. This is used in a study of triaxial extension, simple sheer and an isotropy induced by the electric field.