Investigation on the viscoelastic behaviors of a circular dielectric elastomer membrane undergoing large deformation

Abstract

To explore the time-dependent dissipative behaviors of a circular dielectric elastomer membrane subject to force and voltage, a viscoelastic model is formulated based on the nonlinear theory for dissipative dielectrics. The circular membrane is attached centrally to a light rigid disk and then connected to a fixed rigid ring. When subject to force and voltage, the membrane deforms into an out-of plane shape, undergoing large deformation. The governing equations to describe the large deformation are derived by using energy variational principle while the viscoelasticity of the membrane is describe by a two-unit spring-dashpot model. The evolutions of the considered variables and the deformed shape are illustrated graphically. In calculation, the effects of the voltage and the pre-stretch on the electromechanical behaviors of the membrane are examined and the results show that they significantly influence the electromechanical behaviors of the membrane. It is expected that the present model may provide some guidelines in the design and application of such dielectric elastomer transducers.