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This work lays out the two-potential framework for the constitutive modeling of dielectric elastomers. After its general presentation, where the constraints imposed by even electromechanical coupling, material frame indifference, material symmetry, and entropy imbalance are all spelled out, the framework is utilized to put forth a specific constitutive model for the prominent class of isotropic incompressible dielectric elastomers. The model accounts for the non-Gaussian elasticity and electrostriction typical of such materials, as well as for their deformation-enhanced shear thinning due to viscous dissipation and their time-dependent polarization due to electric dissipation. The key theoretical and practical features of the model are discussed, with special emphasis on its specialization in the limit of small deformations and moderate electric fields. The last part of this paper is devoted to the deployment of the model to fully describe the electromechanical behavior of a commercially significant dielectric elastomer, namely, the acrylate elastomer VHB 4910 from 3M. 

Polymer nanocomposites exhibit unique effective properties that do not follow conventional effective media approaches. The nanoparticle-polymer interphase has been shown to strongly influence the nanocomposites behavior due o its significant volume when the particles are nano-sized, affording an opportunity to tune the dielectric response of the resulting nanocomposite. In this study, we investigate the effects of TiO2 nanoparticles on the electrical properties and the charges distribution and transport in polydimethylsiloxane (PDMS) nanocomposites. Impedance spectroscopy shows suppression of interfacial Maxwell-Wagner-Sillars (MWS) polarization accompanied by a reduction in the low frequency dielectric permittivity and loss at high temperatures in the presence of the TiO2 nanoparticles. Thermally stimulated discharge current measurements confirm that the suppression of the interfacial polarization relaxations happens by redistributing or depleting the charges through the composite and hindering their mobility, potentially resulting in lower electrical conduction and higher breakdown strength. Although the model materials investigated here are TiO2 nanoparticles and Sylgard 184 PDMS, our findings can be extended to other nanoparticulate-filled elastomer composites to design lightweight dielectrics, actuators and sensors with improved capabilities.