Modeling of a pre-stretched dielectric elastomer : A second law of thermodynamics-based approach

Research in smart materials, which have fluid-like properties is playing an increasingly dominant role in the fields of aerodynamics as well as in the fluid power systems. Dielectric elastomers are the smart materials, that demonstrate the deformation behavior similar to the smart solids as well as the fluids depending on the environmental conditions. This necessitates a smart deformation approach, which may analyze the deformation of the continua, accurately. In the present paper, we report an alternative modeling method for the deformation of a continua within the framework of the second law of thermodynamics. We adopt a unified continuum mechanics approach to model the deformation of a pre-stretched dielectric elastomer with an application of the electric field. An analytical electromechanical instability model is formulated for a pre-stretched dielectric elastomer through the standard Neo-Hookean, Mooney-Rivlin, and Gent types of energy density functions. A qualitative comparison between these energy density functions is also presented based on the electromechanical instability of a pre-stretched dielectric elastomer. It is shown based on the obtained results that Gent energy density function shows the instability phenomenon with the chain stiffening effect, and the pre-stretching effect may improve the electromechanical instability of the dielectric elastomers. (paper)