Enhancement of elasto-dielectrics by homogenization of active charges

TL;DR

This paper develops a homogenized model for elasto-dielectric elastomers with micro-charges, demonstrating how tailored microstructures can enhance electric and electrostrictive responses.

Contribution

It introduces a homogenization approach for PDE systems with micro-charges in elastomers, revealing conditions for electric enhancement based on microstructure and charge distribution.

Findings

Homogenized PDE system derived for microstructured elastomers.

Electric enhancement achieved through tailored micro-charge distributions.

Explicit electrostrictive enhancement in dilute regimes.

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.