A variational formulation for electroelasticity of microcontinua

The governing equations for a micromorphic theory of electromagneto-elastic dielectrics are derived by a variational formulation. Balance equations and boundary conditions are obtained assuming the internal energy as dependent on macro and micro-strain variables. A micropolar linear model is derived and the evolution equations for dipole and quadrupole are exploited to arrive at an expression for the polarization density. The present model is applied to the simple shear static problem for an isotropic dielectric layer subject to an external field. The resulting shear displacement and electric potential noticeably differ from the classical elastic case.