Multiscale analysis of the electromechanical coupling in dielectric elastomers

The coupled electromechanical response of dielectrics is analyzed in terms of the local response and the distribution of its microstructural unit elements. A comparison between two variational statements for a continuous and a discrete systems results in an estimate for the macroscopic coupled electromechanical energy-density function. Next, a few types of unit elements are considered and the corresponding behaviors of dielectrics with a random distribution of these elements are calculated. Additionally, to highlight the possible effect of local constraints among the unit elements, a deterministic model for a network of polymer chains is proposed and its response to electric excitation is determined. The practically common case of a uniaxial stretch aligned with the electric field is examined in detail and the results are compared with widely accepted macroscopic models and available experimental results.