Electrostatic Forces and Stored Energy for Deformable Dielectric Materials
Top Cited Papers
Open Access
- 26 August 2004
- journal article
- Published by ASME International in Journal of Applied Mechanics
- Vol. 72 (4), 581-590
- https://doi.org/10.1115/1.1940661
Abstract
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.Keywords
This publication has 16 references indexed in Scilit:
- Derivatives of the Rotation and Stretch TensorsMathematics and Mechanics of Solids, 2004
- High-Speed Electrically Actuated Elastomers with Strain Greater Than 100%Science, 2000
- A phenomenological constitutive law for the behaviour of ferroelectric ceramicsFerroelectrics, 1999
- Large Deformation Isotropic Elasticity—On the Correlation of Theory and Experiment for Incompressible Rubberlike SolidsRubber Chemistry and Technology, 1973
- Large deformation isotropic elasticity: on the correlation of theory and experiment for compressible rubberlike solidsProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1972
- Large deformation isotropic elasticity – on the correlation of theory and experiment for incompressible rubberlike solidsProceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, 1972
- The thermodynamics of elastic materials with heat conduction and viscosityArchive for Rational Mechanics and Analysis, 1963
- Application of Finite Elastic Theory to the Behavior of Rubberlike MaterialsRubber Chemistry and Technology, 1963
- On the foundations of electroelastostaticsInternational Journal of Engineering Science, 1963
- Application of Finite Elastic Theory to the Deformation of Rubbery MaterialsTransactions of the Society of Rheology, 1962