Nonlinear deformation analysis of a dielectric elastomer membrane–spring system

Due to their large strain capability, dielectric elastomers are promising materials for application as transducers in cameras, robots, valves, pumps, energy harvesters, and so on. The dielectric elastomer transducers are based on the deformation of a soft polymer membrane contracting in thickness and expanding in area, induced by the application of a voltage across the two compliant electrodes coated on both sides of the membrane. This paper focuses on the static large deformation analysis of a dielectric elastomer membrane–spring system. The system is constructed from attaching a disk in the middle of a circular dielectric membrane and then connecting the disk with a spring. This configuration can be potentially used as a key part in valves. The basic governing equations describing the large out-of-plane deformations are formulated, and the obtained equations are solved numerically. The relations related to the displacement of the disk, the spring force, the applied voltage, and the parameters of spring including stiffness and initial length are illustrated. The results show that the anticipated displacement of the disk can be controlled by adjusting either or both of the parameters of the spring and the applied voltage. In addition, the parameters of the spring, that is, the stiffness and the initial length, play an important role in the performance of the membrane–spring system.