Micromorphic elastic dielectrics: Linear model and micropolar isotropic thin layers

The micromorphic continuum theory of dielectrics introduced in a previous work (Romeo, 2011) is here reduced to a linear set of balance and constitutive equations modeling thermo-electromagneto-elastic solids which allow for electric dipoles and quadrupoles. Electric polarization turns out to be a linear function of macroscopic strain, microrotation and their gradients. Micropolar isotropic dielectrics are considered in particular to set up the one-dimensional problem of a dielectric layer subjected to a voltage drop. The solution accounts for ionic permeability and electrostriction. In addition, the well known anomalous behavior of the electric capacitance of thin dielectric layers arises as a consequence of electroelastic coupling.