An Energy-Based Approach to Extract the Dynamic Instability Parameters of Dielectric Elastomer Actuators

An energy-based approach is presented to extract the thresholds on the transient dynamic response of step voltage driven dielectric elastomer actuators (DEAs). The proposed approach relies on establishing the energy balance at the point of maximum stretch in an oscillation cycle followed by the application of an instability condition to extract the dynamic instability parameters. Explicit expressions are developed for the critical values of maximum stretch and the corresponding nominal electric field, thus circumventing the need to perform iterative time-integrations of the equation of motion. The underlying principles of the approach are enunciated for the neo-Hookean material model and further extended to analyze relatively complex multiparameter hyperelastic models (Mooney–Rivlin and Ogden) that are employed prevalently for investigating the behavior of DEAs. The dynamic instability parameters predicted using the energy method are validated by examining the time-history response of the actuator in the vicinity of the dynamic instability. The development of dynamic instability parameters is complemented by energy-based extraction of static instability parameters to facilitate a quick comparison between the two. It is inferred quantitatively that the nominal electric field sufficient to cause the dynamic instability and the corresponding thickness stretch is lower than those corresponding to the static instability. A set of representative case studies for multiparameter material models is presented at the end, which can be used as an input for further experimental corroboration. The results of the present investigation can find their potential use in the design of DEAs subjected to transient loading.