Elastic Electric field

Polarization which can be induced in nonconducting materials by means of an externally appHed electric field is one of the most important parameters in the theory of insulators, which are called dielectrics when their polarizabiUty is under consideration (1). Experimental investigations have shown that these materials can be divided into linear and nonlinear dielectrics in accordance with their behavior in a realizable range of the electric field. The electric polarization PI of linear dielectrics depends linearly on the electric field E, whereas that of nonlinear dielectrics is a nonlinear function of the electric field (2). The polarization values which can be measured in linear (normal) dielectrics upon appHcation of experimentally attainable electric fields are usually small. However, a certain group of nonlinear dielectrics exhibit polarization values which are several orders of magnitude larger than those observed in normal dielectrics (3). Consequentiy, a number of useful physical properties related to the polarization of the materials, such as elastic, thermal, optical, electromechanical, etc, are observed in these groups of nonlinear dielectrics (4). 

Many investigators beheve that the Bingham model accounts best for observations of electrorheological behavior (116,118), but other models have also been proposed (116,119). There is considerable evidence that ER materials behave as linear viscoelastic fluids while under the influence of electric field (120) thus it appears that these materials maybe thought of as elastic Bingham fluids. 

The uncoupled response of a piezoelectric sample to elastic shock compression is determined on the assumption that the mechanical response of the material is independent of any electric fields that may be present. In this approximation, a steady shock is introduced into material at rest while the... 

The contribution to the stress from electromechanical coupling is readily estimated from the constitutive relation [Eq. (4.2)]. Under conditions of uniaxial strain and field, and for an open circuit, we find that the elastic stiffness is increased by the multiplying factor (1 -i- K ) where the square of the electromechanical coupling factor for uniaxial strain, is a measure of the stiffening effect of the electric field. Values of for various materials are for x-cut quartz, 0.0008, for z-cut lithium niobate, 0.055 for y-cut lithium niobate, 0.074 for barium titanate ceramic, 0.5 and for PZT-5H ceramic, 0.75. These examples show that electromechanical coupling effects can be expected to vary from barely detectable to quite substantial. 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

The y-cut crystals showed little, if any, output signal under the same conditions for which the z-cut crystals were studied. In this case it should be observed that the y-cut crystals exhibit higher elastic limits and much higher piezoelectric polarizations than the z-cut crystals. These conditions result in much higher electric fields in the elastic region, and these fields are apparently sufficiently large that the crystals were completely conductive internally in the region between the elastic and plastic waves. 

Eckart, criteria, 264, 298 procedure, 267 Effective charge, 274, 276 Effective Hamiltonian, 226 Elastic model, excess entropy calculation from, 141 of a solid solution, 140 Electric correlation, 248 Electric field gradient, 188, 189 Electron (s), 200... 

Sounds and vibrations in electrical appliances or vehicles are in some cases unpleasant. If we can reduce these sounds and vibrations as we desire, we will have a more happy and comfortable life in the next century. Sections 4 and 5 discuss a new smart polymer gel for actively reducing sounds and vibrations. The smart gel can vary its elastic modulus in an electric field. 

Polarization in the point dipole model occurs not at the surface of the particle but within it. If dipoles form in particles, an interaction between dipoles occurs more or less even if they are in a solid-like matrix [48], The interaction becomes strong as the dipoles come close to each other. When the particles contact each other along the applied electric field, the interaction reaches a maximum. A balance between the particle interaction and the elastic modulus of the solid matrix is important for the ER effect to transpire. If the elastic modulus of the solid-like matrix is larger than the sum of the interactions of the particles, the ER effect may not be observed macroscopically. Therefore, the matrix should be a soft material such as gels or elastomers to produce the ER effect. 

From the experimental results, the ER effect in polymer gels is explained as follows (Fig. 8). When an electric field is applied, the particles electrically bind together and cannot slip past each other. Larger shear forces are needed in the presence of an electric field. Thus, the electric field apparently enhances the elastic modulus of the composite gel. The difference in ER effects between an oil and a gel is that the polarized particles necessarily cannot move between the electrodes to produce the ER effect in a gel. In order for the ER effect to occur, it is important to form migration paths before application of an electric field. 

Because an electric field also involves a magnetic field, it is suggested that the materials which increase elastic modulus in external magnetic fields (MR gel) can be prepared using particles which can polarize in a magnetic field. An MR gel will be discussed in Sect. 5.1. 

The elastic modulus of laminated composite plate in which an ER silicone gel of carbonaceous particles is sandwiched between two PVC sheets also changed under the influence of an electric field. It was found that an electric field of 1.17 kV/mm caused a gain in the elastic modulus of the gel of 13% [57]. 

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