CiteULike: norris's eap

Converse electrostriction in polymers and composites

S Eury — 2007-05-23T14:54:12-00:00

pp. 18-23.

The evaluation of electrostrictive properties of low permittivity dielectrics requires extremely sensitive instrumentation. In the present work, a modified compressometer capable of resolving fractional changes in capacitance of the order of 10-6 is used. In the compressometric method, a high sensitivity capacitance bridge, GenRad 1615, is coupled with two lock-in amplifiers to detect attofarad (10-18F) level capacitance changes caused by in-phase cyclic uniaxial stresses on the samples. In studying low-permittivity polymers, we have obtained extensive electrostriction data, which along with widely accepted data on ferroelectric materials and soft polymers, verify the linear relationship between electrostriction coefficient (Q) and the ratio of elastic compliance and dielectric permittivity (s/0r). This leads to an effective way to predict the electrostriction coefficient in dielectric materials.

Some aspects of large strain actuation in dielectric elastomers

G Kofod — 2007-05-23T14:40:46-00:00

Electrets, 2005. ISE-12. 2005 12th International Symposium on (2005), pp. 208-211.

In the search for artificial muscles, a special contender appears to be standing out. The electric field-actuated dielectric elastomer actuators (DEA) display strains well above 100%, with actuation stresses in the MPa region. A DEA is best described as a capacitor made entirely of compliant materials: both the dielectric and the electrodes may stretch. When the capacitor is charged, the attraction between the charged electrodes applies a pressure on the dielectric, known as the Maxwell pressure, p = /spl epsiv//spl epsiv//sub o/E/sup 2/.The dielectric constant and the dielectric breakdown strength are both important. Further, because large strains are desirable, the compliance of the electrodes, as well as of the dielectric material, are crucial. Elastomers are an obvious choice for the dielectric material, and they can be made conducting through the use of conducting fillers. Also, since the strains are so large, the theory describing such actuation is highly non-linear. This article intends to review the theory of DEA, with introductions to a nonlinear high-strain model.

A few remarks on the electrostriction of elastomers

I Krakovsky — 2007-05-23T14:15:58-00:00

Journal of Applied Physics, Vol. 85, No. 1. (1999), pp. 628-629.

The electromechanical behavior of isotropic dielectrics with emphasis on cross-linked polymers (elastomers) as a special case is briefly discussed. Errors often committed in the derivation of expressions used in interpretation of experimental results are pointed out. ©1999 American Institute of Physics.

Simple derivation of the Maxwell stress tensor and electrostrictive effects in crystals

HJ Juretschke — 2007-05-23T14:13:03-00:00

American Journal of Physics, Vol. 45, No. 3. (1977), pp. 277-280.

Local equilibrium and energy considerations in an elastic dielectric crystal lead to a simple derivation of the Maxwell stress tensor in anisotropic dielectric solids. The resulting equilibrium stress–strain relations in the presence of electric fields are applied to determine the deformations of a charged parallel plate capacitor and to find the strains in the capacitor electrodes that accompany the charging.

A Nonlinear Model for Dielectric Elastomer Membranes

Nakhiah Goulbourne — 2007-05-23T14:02:00-00:00

Journal of Applied Mechanics, Vol. 72, No. 6. (2005), pp. 899-906.

The material and geometrical nonlinearities of novel dielectric elastomer actuators make them more difficult to model than linear materials used in traditional actuators. To accurately model dielectric elastomers, a comprehensive mathematical formulation that incorporates large deformations, material nonlinearity, and electrical effects is derived using Maxwell-Faraday electrostatics and nonlinear elasticity. The analytical model is used to numerically solve for the resultant behavior of an inflatable dielectric elastomer membrane, subject to changes in various system parameters such as prestrain, external pressure, applied voltage, and the percentage electroded membrane area. The model can be used to predict acceptable ranges of motion for prescribed system specifications. The predicted trends are qualitatively supported by experimental work on fluid pumps [A. Tews, K. Pope, and A. Snyder, Proceedings SPIE, 2003)]. For a potential cardiac pump application, it is envisioned that the active dielectric elastomer membrane will function as the motive element of the device.

A nonlinear field theory of deformable dielectrics

Zhigang Suo — 2007-05-22T16:26:16-00:00

Journal of the Mechanics and Physics of Solids (2007)

Nonlinear Electroelastic Deformations

A Dorfmann — 2007-05-22T16:12:25-00:00

Journal of Elasticity, Vol. 82, No. 2. (23 February 2006), pp. 99-127.

Abstract Electro-sensitive (ES) elastomers form a class of smart materials whose mechanical properties can be changed rapidly by the application of an electric field. These materials have attracted considerable interest recently because of their potential for providing relatively cheap and light replacements for mechanical devices, such as actuators, and also for the development of artificial muscles. In this paper we are concerned with a theoretical framework for the analysis of boundary-value problems that underpin the applications of the associated electromechanical interactions. We confine attention to the static situation and first summarize the governing equations for a solid material capable of large electroelastic deformations. The general constitutive laws for the Cauchy stress tensor and the electric field vectors for an isotropic electroelastic material are developed in a compact form following recent work by the authors. The equations are then applied, in the case of an incompressible material, to the solution of a number of representative boundary-value problems. Specifically, we consider the influence of a radial electric field on the azimuthal shear response of a thick-walled circular cylindrical tube, the extension and inflation characteristics of the same tube under either a radial or an axial electric field (or both fields combined), and the effect of a radial field on the deformation of an internally pressurized spherical shell.

On nonlinear universal relations in nonlinear elasticity

R Bustamante — 2007-05-22T16:05:35-00:00

Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 57, No. 4. (23 July 2006), pp. 708-721.

Abstract. In the theory of nonlinear elasticity universal relations are relationships connecting the components of stress and deformation tensors that hold independently of the constitutive equation for the considered class (or sub-class) of materials. They are classified as linear or nonlinear according as the components of the stress appear linearly or nonlinearly in the relations. In this paper a general scheme is developed for the derivation of nonlinear universal relations and is applied to the constitutive law of an isotropic Cauchy elastic solid. In particular, we consider examples of quadratic and cubic universal relations. In respect of universal solutions our results confirm the general result of Pucci and Saccomandi [1] that nonlinear universal relations are necessarily generated by the linear ones. On the other hand, for non-universal solutions we develop a general method for generating nonlinear universal relations and illustrate the results in the case of cubic relations.

Universal relations for nonlinear electroelastic solids

R Bustamante — 2007-05-22T16:01:28-00:00

Acta Mechanica, Vol. 182, No. 1. (March 2006), pp. 125-140.

Summary Electro-sensitive elastomers are materials that can support large elastic deformations under the influence of an electric field. There has been growing interest recently in their applications as so-called “smart materials”. This paper is devoted to the derivation of universal relations in the context of the nonlinear theory of electroelasticity that underpins such applications. Universal relations are equations relating the components of the stress, the electric variables and the deformation that are independent of the constitutive law for a family of materials. For the general constitutive equations of an isotropic electroelastic material derived from a free energy function and for some special cases of these equations, we obtain universal relations, the word “universal” being relative to the considered class or subclass of constitutive laws. These universal relations are then applied to some controllable states (homogeneous and non-homogeneous) in order to highlight some examples that may be useful from the point of view of experimental characterization of the material properties. Additionally, we examine the (non-controllable) problem of helical shear of a circular cylindrical tube in the presence of a radial electric field, and we find that a nonlinear universal relation that has been obtained previously for an elastic material also holds when the electric field is applied.

Nonlinear electroelasticity

A Dorfmann — 2007-05-22T15:54:59-00:00

Acta Mechanica, Vol. 174, No. 3. (1 March 2005), pp. 167-183.

Summary. Electro-sensitive (ES) elastomers are “smart materials” whose mechanical properties may be changed significantly by the application of an electric field. In this paper, we provide a theoretical basis for the characterization of the nonlinear electroelastic properties of these materials. The theory is then applied to some simple prototype boundary-value problems in order to illustrate the effect of an electric field on the mechanical response.

Elastic Dielectric

J Grindlay — 2007-05-22T15:52:42-00:00

Physical Review, Vol. 149, No. 2. (1966), 637.

A variational principle is used to derive field equations and boundary conditions for the description of the nonlinear behavior of an elastic dielectric in static equilibrium in an electric field. A discussion of the equilibrium conditions for a rigid dielectric is given to provide a check on the more general theory.

Electrostatic Forces and Stored Energy for Deformable Dielectric Materials

Robert Mcmeeking — 2007-05-22T15:40:15-00:00

Journal of Applied Mechanics, Vol. 72, No. 4. (2005), pp. 581-590.

An isothermal energy balance is formulated for a system consisting of deformable dielectric bodies, electrodes, and the surrounding space. The formulation in this paper is obtained in the electrostatic limit but with the possibility of arbitrarily large deformations of polarizable material. The energy balance recognizes that charges may be driven onto or off of the electrodes, a process accompanied by external electrical work; mechanical loads may be applied to the bodies, thereby doing work through displacements; energy is stored in the material by such features as elasticity of the lattice, piezoelectricity, and dielectric and electrostatic interactions; and nonlinear reversible material behavior such as electrostriction may occur. Thus the external work is balanced by (1) internal energy consisting of stress doing work on strain increments, (2) the energy associated with permeating free space with an electric field, and (3) by the electric field doing work on increments of electric displacement or, equivalently, polarization. For a conservative system, the internal work is stored reversibly in the body and in the underlying and surrounding space. The resulting work statement for a conservative system is considered in the special cases of isotropic deformable dielectrics and piezoelectric materials. We identify the electrostatic stress, which provides measurable information quantifying the electrostatic effects within the system, and find that it is intimately tied to the constitutive formulation for the material and the associated stored energy and cannot be independent of them. The Maxwell stress, which is related to the force exerted by the electric field on charges in the system, cannot be automatically identified with the electrostatic stress and is difficult to measure. Two well-known and one novel formula for the electrostatic stress are identified and related to specific but differing constitutive assumptions for isotropic materials. The electrostatic stress is then obtained for a specific set of assumptions in regard to a piezoelectric material. An exploration of the behavior of an actuator composed of a deformable, electroactive polymer is presented based on the formulation of the paper.

Electrostriction of polymer dielectrics with compliant electrodes as a means of actuation

RE Pelrine — 2007-05-22T15:35:36-00:00

pp. 77-85.

The electrostriction of elastomeric polymer dielectrics with compliant electrodes is potentially useful as a small-scale, solid-state actuator technology. Electrostrictive polymer (EP) materials are capable of efficient and fast response with high strains (> 30%), good actuation pressures (up to 1.9 MPa), and high specific energy densities (up to 0.1 Jg-1). In this article, the mechanism of electrostriction is shown to be due to the electrostatic attraction of free charges on the electrodes. Although EP actuators are electrostatics based, they are shown to produce 5-20 times the effective actuation pressure of conventional air-gap electrostatics at the same electric field strength. The thin uniform dielectric films necessary for fabrication of EP actuators have been fabricated by techniques such as spin coating, casting, and dipping. A variety of materials and techniques have been used to produce the compliant electrodes, including lift-off stenciling techniques for powdered graphite, selective wetting of ionically conductive polymers, and spray coating of carbon blacks and fibrils in polymeric binders. Prototype actuators have been demonstrated in a variety of configurations such as stretched films, stacks, rolls, tubes, and unimorphs. Potential applications of the technology in areas such as microrobots, sound generators, and displays are discussed in this article.

High-field deformation of elastomeric dielectrics for actuators

Ron Pelrine — 2007-05-22T15:31:21-00:00

Materials Science and Engineering: C, Vol. 11, No. 2. (28 November 2000), pp. 89-100.

This paper investigates the use of elastomeric dielectric materials with compliant electrodes as a means of actuation. When a voltage is applied to the electrodes, the elastomeric films expand in area and compresses in thickness. The strain response to applied electric fields was measured for a variety of elastomers. A nonlinear, high-strain, Mooney-Rivlin model was used to determine the expected strain response for a given applied field pressure. Comparing this analytical result to with experimentally measured strains, we determined that the electrostatic forces between the free charges on the electrodes are responsible for the observed response. Silicone polymers have produced the best combination of high strain and energy density, with thickness strains up to 41% and elastic energy densities up to 0.2 MJ/m3. Response times of 2 ms have been experimentally measured. This paper also reports recent progress in making highly compliant electrodes. We have shown, for example, that gold traces fabricated in a zig-zag pattern on silicone retain their conductivity when stretched up to 80%, compared to 1-5% when fabricated as a uniform two-dimensional electrodelayer. Optimal loading of dielectric elastomers can have a significant impact on performance: and the paper describes techniques which that can increase output up to a factor of 5 compared to neutral loading conditions. Lastly, the paper briefly discusses the performance of various actuators that use dielectric elastomer materials. The technology appears to be well-suited to a variety of small-scale actuator applications.

Actuation Response of Polyacrylate Dielectric Elastomers

Guggi Kofod — 2007-05-22T15:24:10-00:00

Journal of Intelligent Material Systems and Structures, Vol. 14, No. 12. (1 December 2003), pp. 787-793.

Polyacrylate dielectric elastomers have yielded extremely large strain and elastic energy density suggesting that they are useful for many actuator applications. A thorough understanding of the physics underlying the mechanism of the observed response to an electric field can help develop improved actuators. The response is believed to be due to Maxwell stress, a quadratic dependence of the stress upon applied electric field. Based on this supposition, an equation relating the applied voltage to the measured force from an actuator was derived. Experimental data fit with the expected behavior, though there are discrepancies. Further analysis suggests that these arise mostly from imperfect manufacture of the actuators, though there is a small contribution from an explicitly electrostrictive behavior of the acrylic adhesive. Measurements of the dielectric constant of stretched polymer reveal that the dielectric constant drops, when the polymer is strained, indicating the existence of a small electrostrictive effect. Finally, measurements of the electric breakdown field were made. These also show a dependence upon the strain. In the unstrained state the breakdown field is 20 MV/m, which grows to 218 MV/m at 500 500% strain. This large increase could prove to be of importance in actuator design. 10.1177/104538903039260

Electrostriction of a Polyurethane Elastomer-Based Polyester

I Diaconu — 2007-04-25T16:20:36-00:00

Sensors Journal, IEEE, Vol. 6, No. 4. (2006), pp. 876-880.

This paper is dealing with the electromechanical properties of a synthesized polyurethane elastomer film-based polyester. On the basis of the electrostatic-field induced strain, dielectric, and stress-strain measurements carried out under ambient conditions, the electromechanical parameters such as thickness strain, apparent electrostrictive coefficient, effective pressure, mechanical energy density, and Maxwell-effect contribution, were determined. Thickness strain versus the static electric field showed a quadratic dependence up to about 6.3 MV/m, which is consistent with an electrostrictive response. The maximum induced strain of 7% obtained at 16 MV/m is higher than those reported in the literature on unprestrained polyurethane film with noncompliant electrodes. Remarkable apparent electrostrictive coefficient<tex>$(sim 7.75 10^-16 hboxm^2/hboxV^2)$</tex>and response time (600 ms) were found. Under the actual experimental conditions (rigid electrodes and maximum electrostatic field of 16 MV/m), the effective compressive pressure (0.9 MPa) and mechanical energy density (0.032<tex>$hboxJ/cm^3$</tex>) values are quite noticeable. A small Maxwell-effect contribution of only 0.32% was found. The electromechanical parameters of this polyurethane elastomer indicate that this material is potentially useful for practical actuators and sensors.

Space charge distribution in bending-electrostrictive polyurethane films doped with salts

Masashi Watanabe — 2007-04-25T16:10:01-00:00

Journal of Polymer Science Part B: Polymer Physics, Vol. 42, No. 3. (2004), pp. 523-531.

Polyurethane films bent during a field application (1.5 MV/m). Doping the films with salts controlled the bending direction. With ZnBr2, Zn(ClO4)2, and Cu(ClO4)2 as the dopants, the films bent to the anode side. Contrarily, CH3COONa-doped, NaBr-doped, and undoped films bent to the cathode side. We also measured the space charge distribution in the films to clarify the factor that determined the direction. The measurements were carried out with a pulsed electroacoustic method. For the films that bent to the anode side, a positive space charge was observed inside the cathode during the field application. However, for the films that bent to the cathode side, there was a negative space charge inside the anode. Thus, the dopants also controlled the space charge distribution, which corresponded to the bending direction. These results suggested a causality between the field-induced bend of the film and the space charge distribution. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 523-531, 2004

Space-charge-enhanced electromechanical response in thin-film polyurethane elastomers

J Su — 2007-04-25T15:57:21-00:00

Applied Physics Letters, Vol. 71, No. 3. (1997), pp. 386-388.

We show that the large electrical-field-induced strain response observed in certain polyurethane elastomers is a thin-film effect. Based on the frequency dispersion of the strain response in samples with different thicknesses and the thermally stimulated discharge current on samples with different processing conditions, we suggest that the charge injection, an interface effect, which results in a nonuniform space-charge distribution and, hence, a nonuniform electric-field distribution across the sample thickness, is responsible for the enhanced electromechanical response in thin polyurethane samples. ©1997 American Institute of Physics.

Electrostrictive effect in polyurethanes

FM Guillot — 2007-04-25T15:50:56-00:00

Journal of Applied Polymer Science, Vol. 89, No. 2. (2003), pp. 399-404.

Polyurethane electrostriction was investigated by measuring the tensile electromechanical coupling coefficients of structurally different materials. True values of the strain coefficients M3311, M3322, and M3333 were obtained for four types of polymer: one commercial polyurethane (DOW 2103-80 AE) and three polyurethanes synthesized at the Naval Surface Warfare Center, including two phase-separated (PS) materials with molecular weights of 1000 and 2000 and one phase-mixed (PM) material with a molecular weight of 2000. Measurements were performed at 2 kHz under a bias field of 4 MV/m at room temperature. Measured values of M3333 ranged from -9.4 × 10-18 to -74.6 × 10-18 m2/V2, with the PM material exhibiting the largest coefficient. The electrostatic interaction (Maxwell stress) did not account for more than 15% of the total electromechanical activity in any of the materials. Furthermore, at the macroscopic level, an empirical relationship was established to predict the values of the electrostrictive coefficients from the dielectric constants and the compliance coefficients of the material. Finally, results indicated that, at the microscopic level, the phenomenon of electrostriction in polyurethanes could be best explained by the presence of charges inside the material (space-charge theory). © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 89: 399-404, 2003

Measurement of electrostrictive coefficients of polymer films

Francois Guillot — 2007-04-25T15:44:39-00:00

The Journal of the Acoustical Society of America, Vol. 110, No. 6. (2001), pp. 2980-2990.

A new technique to experimentally determine the electrostrictive coefficients of thin polymer films is presented. This technique is a second-order extension of the first-order quasistatic method for the measurement of piezoelectric coefficients previously introduced by Guillot and Jarzynski [J. Acoust. Soc. Am. 108, 600–607 (2000)]. In the present method, electrically induced strains are measured optically on a rubber-encapsulated sample. These strains are used in a Rayleigh–Ritz procedure that minimizes the total energy of the sample and whose output is a set of three tensile electrostrictive coefficients. The total energy of the sample includes elastic contributions from the polymer and the encapsulating rubber as well as two quadratic electromechanical terms corresponding to Maxwell stress and to electrostriction. Therefore, the external electrostatic effects can be separated from the intrinsic electrostrictive behavior, and the measured coefficients are true material properties. Data obtained on two types of polyurethanes submitted to a bias field of approximately 4 MV/m at 2 kHz and at room temperature are presented. It was found that these materials possess very large electrostrictive coefficients and that the Maxwell stress effect is responsible for less than 13% of their total electromechanical behavior. ©2001 Acoustical Society of America.

Electrostriction of Polar Glasses

JI Katz — 2007-04-22T18:29:28-00:00

(30 May 1996)

We develop a finite temperature theory for the susceptibility and electrostriction of isotropic substances in which permanent electric dipoles are restrained from free rotation by elastic forces. All parameters are constrained by the measured susceptibility and elastic constants. When applied to polyurethane, the predicted electrostriction is approximately consistent wiht some of the wide range of data. The saturation of the electrostriction at high field may be explained qualitatively if the dipoles consist of several amide groups locked together by crystallization of the hard segments of the polymer.