Dielectric elastomers are attractive materials for sensors and actuators in haptic, acoustic, medical or robotic applications. The dielectric elastomers are often used in form of prestreched membranes with compliant electrodes activated by an electric voltage. The hereby occuring Maxwell stresses lead to a compression of the DE membrane an can produce electro-mechanical instabilities, which can initiate a failure of the system, if a critical compression is reached and the electric field is continuously increasing. Viscous material properties can influence this failure mechanism, in literature denoted as pull-in instability.
In this work we will present the equation of motion for a dissipative dielectric elastomer actuator (DEA) system and the evolution of the viscous variable, derived from the Euler-Lagrange formalism. Moreover, the stability analysis will be shown to extract the critical values of pull-in instability, for both the quasi-static and the dynamic case. Numerical results will be shown to demonstrate the instability and dynamic behavior of an in-plane preloaded homogeneous viscous hyperelastic DEA under excitation of step voltage and sinusoidally oscillating voltage. Particularly, the influence of viscoelasticity and biaxial in-plane prestretch will be studied.