Effect of the deformation dependent permittivity on the actuation of a pre-stretched circular dielectric actuator

Abstract

Experiments have shown that under large deformation, the permittivity of some dielectric elastomers demonstrates significant deformation dependent behavior. In this paper, we theoretically analyze the effect of this behavior on the actuation of a circular actuator made of a dielectric elastomer, VHB 4910. The dependency of permittivity on deformation is considered through the equations of state. The equilibrium equations of the actuator are solved by MATLAB. The electromechanical instability, loss of tension and dielectric breakdown of the actuator during the actuation process under different pre-stretch levels are discussed. It is found that the dependency of permittivity on deformation can effectively suppress the electromechanical instability of the actuator at low pre-stretch levels. At high pre-stretch levels, however, it lowers the maximum stretch the actuator can achieve. Compared to the case of a constant permittivity, the deformation-dependent effect results in higher voltage needed to achieve the same actuated stretch, and this discrepancy in voltage increases as the pre-stretch increases. Furthermore, it is found that the maximum achievable stretch and the corresponding voltage show a strong dependence on factor c in the permittivity-stretch relation, while the stretch at the onset of loss of tension is independent of c.