Elastic dielectric

In the plus-x orientation, the region behind the plastic wave is treated as a conductor. Accordingly, in the electrical model, the left electrode is moving with the velocity of the plastic wave. Otherwise, the analysis proceeds as in the case of the elastic-dielectric. For convenience it is assumed that 3 = 2 = i. The thicknesses of the two dielectric regions are = I and I2 — ([/, — U2)t. Solution for the current is then... 

The current pulse described in Eq. (5.1) is markedly different from that describing the elastic-dielectric. Particular features of the solution may be characterized by solutions for current j, at times t = 0 and if at time t/Uy. They are... 

Equation 5.2 indicates that i is much lower than the corresponding value for the elastic-dielectric, while Eq. (5.3) indicates that if is significantly greater than the corresponding value for the elastic-dielectric. Since both of these current values depend upon the velocity of the plastic wave, measurements of these currents can, in principle, be used to evaluate the velocity of the plastic wave. Observation of a waveform described by Eq. (5.1) would confirm the presence of a second wave behind which the material is conductive. 

Interpretation of the experimental study of quartz leads to the conclusions that below 6 GPa and greater than 2.5 GPa x-cut quartz responds as an approximation to the elastic-dielectric model, but that there are very signifi-... 

A. Bogi and S. Faetti, Elastic, dielectric and optical constants of 4 -pentyl-4-cyanobiphenyl, Liq. Cryst., 28 (2001) 729-739. 

Mason (1355) determined the elastic, dielectric, and piezoelectric constants of potassium and ammonium dihydrogen phosphate. He concluded that there are two distinct sets of H bonds in the ammonium salt—one set (N—H to O of PO4) is influential in thermal and specific heat anomalies, and the other set (part of the H2PO4 groups) affects the dielectric and piezoelectric properties. As mentioned earlier, a H... 

Recent work showed [30] that in this case EC sets in with a continuous transition from the homogeneous state directly, similarly to the classical configuration of case A. It has been shown that the pattern forming mechanism, including the role of the elastic, dielectric, viscous and CH terms, is analogous to that of case A, and the standard model is applicable. The anal34ical one-mode neutral-curve expression for homeotropic initial alignment [31] is as follows ... 

The elastic, dielectric and magnetic torques can be evaluated from the functional derivative... 

Zhao X, Suo Z (2008) Electrostriction in elastic dielectrics undergoing large deformation. 

Schlaak HF, Jungmann M, Matysek M, Lotz P (2005) Novel multilayer electrostatic solid state actuators with elastic dielectric. Proc SPIE 5759 121... 

The foimdations of the thermodynamic theory of elastic dielectrics and of piezoelectricity were laid down by Toupiir, Eringen, Hajicek, Grindlay and other researchers (Tichy and Gautschi 1980) in the second half of the twentieth century. Both experimental and theoretical research of rron-hnear effects in dielectrics is being continued even today (Kittinger and Tichy 1992 Nelson 1979). 

The base vectors of an elementary cell in a translation lattice together with one lattice point define a crystollogrophic coordinote system, which is suitable for description of crystallographic planes and directions by means of vectors with integer components. But for description of crystal pltysical properties (e.g. elastic, dielectric or pyroelectric properties, etc.) rising material constants another coordinate system, so called the Cortesion system, is preferred. 

The purpose of this chapter is to extend the macroscopic description of the mechanical-thermodynamical behaviour of matter to elastic dielectrics with piezoelectric properties. This step allows then the study of electromechanical interactions forming the basis of piezoelectric elements in force, pressure, and acceleration sensors. 

This relation is the basis of the thermodynamics of an elastic dielectric. Components Z), and Ei are rrrriquely defined for a certain thermodynamic eqiri-librium state and, therefore, take the place of additional variables of state in the thermo namic sense. In what follows we will use the simple term variable to designate a thermodynamic state variable unless the distinction becomes necessary. 

Hajicek P (1968) On the thermodynamic potentials of elastic dielectrics. Czech J Phys B18 1008-1010... 

Toupin RA (1956) The elastic dielectric. J Ration Mech Anal 5 849... 

Bailey DS, Soluch W, Lee DL, Vetelino JF, Andie J, Chai BHT (1982) The elastic, dielectric and piezoelectric constants of berlinite. Proceedings of 36th Annual Frequency Control Symposium, pp 124-132... 

Shanthi M, Lim LC, Rajan KK, Jin J (2008) Complete sets of elastic, dielectric, and piezoelectric properties of flux-grown [011]-poled PMN-(28-32)%PT single crystals. Appl Phys Lett 92 142906... 

Jungmann, M. Matysek, M. Schlaak, H.F. Electrostatic solid-state actuators with elastic dielectric and multilayer fabrication-technology. Proc. Actuator 2004, 14-16 June 2004, Bremen (2004), pp. 686-689... 

The condition of equilibrium of the three torques, elastic, dielectric, and fiexoelectric, coincides with the equation of the director rotation. In view of approximation (5.78) it gives... 

Omote, K., Ohigashi, H. and Koga, K. (1997) Temperature dependence of elastic, dielectric and piezoelectric properties of single crystalline films of vinylidene fluoride trifluoroethylene copolymer, J. App. Phys, 81, 2760-9. 

Roussel M, Malhaire C, Deman A-L et al (2014) Electromechanical study of polyurethane films with carbon black nanoparticles for MEMS actuators. J Micromech Microeng 24 055011 Schlaak HF, Jungmann M, Matysek M et al (2005) Novel multilayer electrostatic solid-state actuators with elastic dielectric. Proc SPIE 5759 121-133 Shian S, Diebold RM, McNamara A et al (2012) Highly compliant transparent electrodes. Appl Phys Lett 101 061101... 

As described above, dielectric elastomers consist of two comphant electrodes which embed an elastic dielectric. When the electrodes are supphed with a voltage V, the electrical field will cause the electrical charges on the electrodes to attract one another. In fact, the electrodes squeeze the dielectric, resulting in an electrostatic pressure pei- Since the dielectric is incompressible, the elastomer film contracts in thickness and expands in area as shown in Fig. 5. 

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