Electromechanical stability of compressible dielectric elastomer actuators

Abstract

The constitutive relation and the electromechanical stability of Varga-Blatz-Ko-type compressible isotropic dielectric elastomers undergoing large deformation are investigated in this paper. Free energy in any form, which consists of elastic strain energy and electric field energy, can be applied to analyze the electromechanical stability of dielectric elastomers. The constitutive relation and the electromechanical stability are analyzed by applying a new kind of free energy model, which consists of elastic strain energy, composed of the Varga model as the volume conservative energy and the Blatz-Ko model as the volume non-conservative energy, and electric field energy with constant permittivity. The ratio between the principal planar stretches, the ratio between the thickness and length direction stretches, and the power exponent of the stretch are defined to characterize the mechanical loading behavior and compressible behavior of the dielectric elastomer. Along with the increase of these parameters, which determine the shape or volume of the elastomer, and the Poisson ratio, the critical nominal electric field is higher, which indicates a more stable dielectric elastomer electromechanical system. In contrast, with the decrease of the dimensionless material parameter α of the Varga elastic strain energy, the critical nominal electric field increases. The coupling system becomes more stable. We further demonstrate that the critical nominal electric field of the compressible dielectric elastomer electromechanical coupling system is significantly influenced by the ratio between the principal planar stretches.