Electro-mechanical analysis of a dielectric elastomer membrane undergoing large deformation

Abstract

In the family of smart material transducers, muscle-like transducers, i.e., dielectric elastomer transducers, have attracted much interest in recent years due to their many fascinating attributes such as large strain, fast response, high efficiency, simple, potentially low cost and light. The essential part of dielectric elastomer transducers is a dielectric membrane sandwiched between two compliant electrodes. Subject to a voltage, the dielectric membrane reduces its thickness and expands its area, converting electrical energy into mechanical energy. Due to large deformation, nonlinear equations of state, and diverse modes of failure, modeling the electro-mechanical response for dielectric elastomer transducers has been challenging. In this paper, the electro-mechanical behavior of a dielectric membrane deformed by the application of voltage and weight into an out-f-plane, axisymmetric shape is investigated. Ogden model is adopted to formulate the state equations by combining kinematics and thermodynamics. A set of ordinary differential equations characterizing the large out-of-plane deformation of the dielectric membrane are derived, and shooting method is applied to solving the equations numerically. The obtained results show that the field in the membrane is very inhomogeneous, which leads to most part of the membrane functioning inefficiently. This can be used to optimize the design of electromechanical transducers for specific applications.