Enhancement of elasto-dielectrics by homogenization of active charges

Abstract

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.

The title of the article has been changed and two parts have been added: the rigorous proof of arbitrarily large dielectric and elastrostrictic enhancement in a dilute regime (Section 5), and the extension of the results to the case of random inclusions (Appendix A)