  We investigate the PDE system resulting from even electromechanical coupling
in elastomers. Assuming a periodic microstructure and a periodic distribution
of micro-charges of a prescribed order, we derive the homogenized system. The
results depend crucially on periodicity (or adequate randomness) and on the
type of microstructure under consideration. We also show electric enhancement
if the charges are carefully tailored to the homogenized electric field and
explicit that enhancement, as well as the corresponding electrostrictive
enhancement in a dilute regime.
