Topic

# Electric displacement field

About: Electric displacement field is a research topic. Over the lifetime, 1525 publications have been published within this topic receiving 29315 citations. The topic is also known as: electric flux density & electric displacement field.

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TL;DR: It is demonstrated that a very high energy density with fast discharge speed and low loss can be obtained in defect-modified poly(vinylidene fluoride) polymers by combining nonpolar and polar molecular structural changes of the polymer with the proper dielectric constants.

Abstract: Dielectric polymers with high dipole density have the potential to achieve very high energy density, which is required in many modern electronics and electric systems. We demonstrate that a very high energy density with fast discharge speed and low loss can be obtained in defect-modified poly(vinylidene fluoride) polymers. This is achieved by combining nonpolar and polar molecular structural changes of the polymer with the proper dielectric constants, to avoid the electric displacement saturation at electric fields well below the breakdown field. The results indicate that a very high dielectric constant may not be desirable to reach a very high energy density.

2,008 citations

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TL;DR: In this article, a closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium, along with a path-independent integral integral of fracture mechanics.

Abstract: A conservation law that leads to a path-independent integral of fracture mechanics is derived along with the governing equations and boundary conditions for linear piezoelectric materials. A closed-form solution to the antiplane fracture problem is obtained for an unbounded piezoelectric medium

732 citations

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TL;DR: In this article, lead lanthanum zirconate titanate (PLZT) was loaded with compressive stress parallel to the polarization and the stress vs strain curve was recorded.

Abstract: Ferroelectric and ferroelastic switching cause ferroelectric ceramics to depolarize and deform when subjected to excessive electric field or stress. Switching is the source of the classic butterfly shaped strain vs electric field curves and the corresponding electric displacement vs electric field loops [1]. It is also the source of a stress—strain curve with linear elastic behavior at low stress, non-linear switching strain at intermediate stress, and linear elastic behavior at high stress [2, 3]. In this work, ceramic lead lanthanum zirconate titanate (PLZT) is polarized by loading with a strong electric field. The resulting strain and polarization hysteresis loops are recorded. The polarized sample is then loaded with compressive stress parallel to the polarization and the stress vs strain curve is recorded. The experimental results are modeled with a computer simulation of the ceramic microstructure. The polarization and strain for an individual grain are predicted from the imposed electric field and stress through a Preisach hysteresis model. The response of the bulk ceramic to applied loads is predicted by averaging the response of individual grains that are considered to be statistically random in orientation. The observed strain and electric displacement hysteresis loops and the nonlinear stress—strain curve for the polycrystalline ceramic are reproduced by the simulation.

651 citations

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TL;DR: In this article, a new formulation of the field theory of dielectric solids is proposed, which does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences.

Abstract: Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell–Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.

485 citations

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TL;DR: In this article, an isothermal energy balance is formulated for a system consisting of deformable dielectric bodies, electrodes, and the surrounding space, which is obtained in the electrostatic limit but with the possibility of arbitrarily large deformations of polarizable material.

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 (I) 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.

388 citations