NONEQUILIBRIUM THERMODYNAMICS OF DIELECTRIC ELASTOMERS
Xuanhe Zhao, Soo Jin Adrian Koh, Zhigang Suo

Abstract
This paper describes an approach to construct models of dielectric elastomers undergoing dissipative processes, such as viscoelastic, dielectric and conductive relaxation. The approach is guided by nonequilibrium thermodynamics, characterizing the state of a dielectric elastomer with kinematic variables through which external loads do work, as well as internal variables that describe the dissipative processes.

Theory of dielectric elastomers capable of giant deformation of actuation
Xuanhe Zhao, Zhigang Suo
Physical Review Letters, 104, 178302 (2010)

The deformation of a dielectric induced by voltage is limited by electrical breakdown if the dielectric is stiff, and by electromechanical instability if the dielectric is compliant. The interplay of the two modes of instability is analyzed for a dielectric elastomer, which is compliant at a small stretch, but stiffens steeply. The theory is illustrated with recent experiments of interpenetrating networks, and with a model of swollen elastomers. The theory predicts that, for an elastomer with a stress-stretch curve of a desirable form, the voltage can induce giant deformation.

Electromechanical instability in semicrystalline polymers
Xuanhe Zhao , Zhigang Suo
Abstract
When a layer of a semicrystalline polymer is subject to a tensile force in its plane and a voltage through its thickness, the deformation of the layer is initially homogeneous,but then localizes.

      This paper studies a gel formed by a network of cross-linked polymers and a species of mobile molecules. The gel is taken to be a dielectric, in which both the polymers and the mobile molecules are nonionic. We formulate a theory of the gel in contact with a solvent made of the mobile molecules, and subject to electromechanical loads. A free-energy function is constructed for an ideal dielectric gel, including contributions from stretching the network, mixing the polymers and the small molecules, and polarizing the gel. We show that the free-energy function is non-convex, leading to instabilities. We also show that mechanical constraint markedly affects the behavior of the gel.

      This letter describes a method to analyze electromechanical stability of dielectric elastomer actuators.  We write the free energy of an actuator using stretches and nominal electric displacement as generalized coordinates, and pre-stresses and voltage as control parameters.  When the Hessian of the free-energy function ceases to be positive-definite, the actuator thins down drastically, often resulting in electrical breakdown.  Our calculation shows that stability of the actuator is markedly enhanced by pre-stresses.

Active polymers are being developed to mimic a salient feature of life: movement in response to stimuli. Large deformation can lead to intriguing phenomena; for example, recent experiments have shown that a voltage can deform a layer of a dielectric elastomer into two coexistent states, one being flat and the other wrinkled. This observation, as well as the needs to analyze large deformation under diverse stimuli, has led us to reexamine the theory of electromechanics. In his classic text, Maxwell showed that electric forces between conductors in a vacuum could be calculated using a field of stress in the vacuum. The Maxwell stress has since been invoked in deformable dielectrics. This practice has been on an insecure theoretical foundation.