Modeling of a pre-strained circular actuator made of dielectric elastomers

Dielectric elastomers are used for the realization of actuators with large deformations and belong to the group of so-called electroactive polymers (EAP). Models are required for the design and optimization of EAP actuators. Thereby the constitutive behavior of the elastomer is of crucial importance and typically uniaxial experiments are performed in order to determine the mechanical properties of these materials. In this paper a pre-strained circular actuator made of a dielectric elastomer is investigated: constitutive models based on uniaxial data are verified by comparing calculation results with experimental observations. An analytical model is derived for the instantaneous response to an activation voltage in the pre-strained circular actuator and a finite element model is used to simulate the time-dependent behavior. Hyperelastic models are used and three strain energy formulations (Yeoh, Ogden and Mooney-Rivlin) are compared in their predictive capabilities. The results of the calculations with the three strain energy forms differ significantly, although all forms were successfully fitted to the same uniaxial data set. Predictions of the actuator behavior with the Yeoh form agree to a great extent with the measurements. The results of the present work show that the circular actuator set-up represents a valid model system for the characterization and optimization of the electromechanical behavior of dielectric elastomers.