A Nonlinear Model for Dielectric Elastomer Membranes

Abstract

The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.