Different formulations of the constitutive laws and governing equations for nonlinear electroelastic solids are reviewed and two new variational principles for electroelastostatics are introduced. One is based on use of the electrostatic scalar potential and one on the vector potential, combined with the deformation function. In each case Lagrangian forms of the electric variables are used. Their connections with several formulations of nonlinear electroelasticity in the literature are established and some differences highlighted.
Bustamante, R., Dorfmann, A., & Ogden, R. W. (2009). Nonlinear electroelastostatics: a variational framework. Zeitschrift für Angewandte Mathematik und Physik, 60(1), 154-177. https://doi.org/10.1007/s00033-007-7145-0