Electromechanical stability of a Mooney-Rivlin-type dielectric elastomer with nonlinear variable permittivity

The electromechanical stability of a Mooney–Rivlin‐type dielectric elastomer undergoing large deformation with nonlinear permittivity is investigated. The stability is analyzed by applying a new kind of free energy model, which couples Ogden elastic strain energy and electric field energy density with nonlinear permittivity. Then, nominal electric field and nominal electric displacement of the dielectric elastomer are introduced. Based on this, the electromechanical stability of the Mooney–Rivlin‐type dielectric elastomer is analyzed by simplifying the Ogden elastic strain energy. The critical breakdown electric fields under the conditions of two stretching ratios and various material constant ratios k (n = km, where m and n are material constants in the Ogden model, determined experimentally) are also obtained. According to the simulation results, for a larger dimensionless constant k of the dielectric material, the critical nominal electric field is higher, the corresponding dielectric elastomer or structure is more stable and the electromechanical stability of the dielectric elastomer is proved to be markedly enhanced by a pre‐stretching process. These results agree well with experimental data and can be used as guidance in the design and fabrication of dielectric elastomer actuators. Copyright © 2010 Society of Chemical Industry Our research represent the relationship between ${D^{\sim}\over \sqrt{m\varepsilon_{0}}}$ and ${E^{\sim}\over \sqrt{m\Big/\varepsilon_{0}}}$ when λ1 = λ2 = λ, S∼⩽16 and k = 1. With ${s\over m}$ (0, 0.5, 1, 1.5, 2, 2.5) increasing, nominal electric field decreases. The shows that pre‐stretch can be enforced to improve stability of dielectric elastomers.