I’ve just come back from EuroEAP 2011, the First International Conference on Electromechanically Active Polymer (EAP) Transducers & Artificial Muscles.  The technical program was exciting.  The meeting was chaired by Federico Carpi, and took place in Pisa, Italy.  The weather was cool, and air fresh. 

Also in the air was optimism for the new technology of dielectric elastomer transducers.   The potential of soft dielectrics as a broad-ranging technology was first brought into focus by a SRI team in a paper published in Science in 2000.  The technology is based on an extremely robust electromechanical coupling.  A membrane of a dielectric elastomer is sandwiched between two compliant electrodes, such as those made of carbon grease.  When a voltage is applied between the two electrodes, one electrode becomes positively charged, and the other becomes negatively charged.  The opposite charges cause the membrane to reduce thickness and expand area.  Linear strains beyond 100% have been achieved.  Many videos of dielectric elastomer transducers are available on YouTube.

A dielectric elastomer is capable of giant electromechanical actuation but fails at breakdown due to instability under certain conditions with a small deformation. By applying a mechanical pre-stretch, one obtains a stabilized large actuation.

In this paper, we measured the dielectric constant and critical voltage of a polyacrylic dielectric elastomer subject to both equal and unequal biaxial stretch, and modelled its actuation by employing the Gent strain energy function with a microscopic view to characterize the nonlinear stiffening behaviour and the electrostrictive effect in the deformation.

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.

In response to a stimulus, a soft material deforms, and the deformation provides a function. We call such a material a soft active material (SAM). This review focuses on one class of soft active materials: dielectric elastomers. Subject to a voltage, a membrane of a dielectric elastomer reduces thickness and expands area, possibly straining over 100%. The phenomenon is being developed as transducers for broad applications, including soft robots, adaptive optics, Braille displays, and electric generators.

This paper analyzes a membrane of a dielectric elastomer, prestretched and mounted on a rigid circular ring, and then inflated by a combination of pressure and voltage. Equations of motion are derived from a nonlinear field theory, and used to analyze several experimental conditions. When the pressure and voltage are static, the membrane may attain a state of equilibrium, around which the membrane can oscillate. The natural frequencies can be tuned by varying the prestretch, pressure, or voltage. A sinusoidal pressure or voltage may excite superharmonic, harmonic, and subharmonic resonance. Several modes of oscillation predicted by the model have not been reported experimentally, possibly because these modes have small deflections, despite large stretches.

International Journal of Solids and Structures. In press.

Dielectric elastomer, as an important category of electroactive polymers, is known to have viscoelastic properties that strongly affect its dynamic performance and limit its application. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principals of nonequilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit.

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.

I’ve just come back from a Winter School on Dielectric Elastomer Transducers, held at Monte Verità, Ascona, Switzerland, 10-16 January 2010.  Lectures were given by various people, covering the theory of electromechanical interaction, design of devices, development of materials, and technologies of manufacturing.  I was asked to give three lectures on the theory.  I attach the slides of my lectures.

Recent experiments have shown that a voltage can induce a large deformation in an elastomer of interpenetrating networks. We describe a model of interpenetrating networks of long and short chains. As the voltage ramps up, the elastomer may undergo a snap-through instability. The network with long chains fills the space and keeps elastomer compliant at small to modest deformation. The network with short chains acts as a safety net that restrains the elastomer from thinning down excessively, averting electrical breakdown.  It appears possible to find a dielectric elastomer capable of giant deformation of actuation.  You can read the paper, or take a look at the slides posted here.

Mechanical energy can be converted to electrical energy by using a dielectric elastomer generator.  The elastomer is susceptible to various modes of failure, including electrical breakdown, electromechanical instability, loss of tension, and rupture by stretch.  The modes of failure define a cycle of maximal energy that can be converted.  This cycle is represented on planes of work-conjugate coordinates, and may be used to guide the design of practical cycles.

As a complement to the current issue of journal club, I would like to bring your attention to our current work on dielectric elastomers. 

Xuanhe Zhao and Zhigang Suo A layer of a dielectric elastomer expands its area when a voltage is applied across its thickness.  The layer can be programmed to deform in three dimensions by using patterned prestretches, electrodes, and stiffeners. 

Xuanhe Zhao and Zhigang Suo  We develop a thermodynamic model of electrostriction for elastic dielectrics capable of large deformation. The model reproduces the classical equations of state for dielectrics at small deformation, but shows that some electrostrictive effects negligible at small deformation may become pronounced at large deformation.

Subject to a voltage, a dielectric elastomer can deform substantially, making it a desirable material for actuators. Designing such an actuator, however, has been challenging due to nonlinear equations of state, as well as multiple modes of failure, parameters of design, and measures of performance. This paper explores these issues, using a spring-roll actuator as an example. We formulate the equations of state of two degrees of freedom, and describe the constraints due to several modes of failure of the elastomer, including electrical breakdown, electromechanical instability, loss of tension, and tensile rupture. Also included is the compressive limit of the spring.

Rob Wood teaches a course on micro/nano robotics, and asks me to give a 30-minute tutorial on the theory of dielectric elastomer actuators (DEAs).  I attach my slides, which might be useful to you if you'd like to include this topic in your class.  The tutorial draws upon work in the literature, as well as recent work in my group: