Dielectric elastomers are capable of large deformation subject to an electric voltage, and are promising for uses as actuators, sensors and generators. Because of large deformation, nonlinear equations of state, and diverse modes of failure, modeling the process of electromechanical transduction has been challenging.  This paper studies a membrane of a dielectric elastomer deformed into an out-of-plane, axisymmetric shape, a configuration used in a family of commercial devices known as the Universal Muscle Actuators. 

The kinematics of deformation and charging, together with thermodynamics, lead to field equations that govern the state of equilibrium, as well as the conditions under which the state of equilibrium is stable.  Numerical results indicate that the field in the membrane can be very inhomogeneous, and that the membrane is susceptible to several modes of failure, including electrical breakdown, electromechanical instability, loss of tension, and rupture by stretch.  Care is needed in design to balance the requirements of averting various modes of failure while using the material efficiently.