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.
