Coupling electromechanical

Remark 4-3. The electromechanical coupling in the materials will be assumed to be linear. 

The subsequent characterization of electromechanical coupling covers the various classes of piezoelectric materials. Details with respect to definition and determination of the constants describing these materials have been standardized by the Institute of Electrical and Electronics Engineers [f04]. Stresses J and strains e on the mechanical side, as well as flux density D and field strength E on the electrostatic side, may be arbitrarily combined into four forms of coupled constitutive equations  

For the subsequent classification of the appearing constants, their determination by means of a test specimen should be kept in mind. The mechanical conditions of constant strain, satisfied by clamped configurations, are designated by ( ) and those of constant stress, satisfied by free boimdaries, by ( ) . The electrostatic conditions of constant field strength, satisfied with short circuited electrodes, are designated by ( )- and those of constant flux density, satisfied with open circuited electrodes, by (). The constants of the matrices e and d thus stand, respectively, for induced stress and strain, whereas the constants of the matrices h and g represent, respectively, sensed stress and strain. While the constitutive matrices of Eqs. (4.10a) and (4.10b) may be converted into one another by complete inversion, the sub-matrices within each line can be transformed as given below  

It is the forms of constitutive equations given by Eqs. (4.10a) that are used most often.The one on the left-hand side is suggested by the formulation of the virtual work of internal contributions in Eq. (3.63). 

Regulation of contractile force by changes in is called electromechanical coupling. This type of regulation primarily involves changes in [Ca +Jj. 

Depolarization (e.g., by action potentials or change in [K+] J increases smooth muscle [Ca +Jj primarily by activation of L-type Ca + channels (Hermsmeyer etai, 

---

Uncoupled solutions for current and electric field give simple and explicit descriptions of the response of piezoelectric solids to shock compression, but the neglect of the influence of the electric field on mechanical behavior (i.e., the electromechanical coupling effects) is a troublesome inconsistency. A first step toward an improved solution is a weak-coupling approximation in which it is recognized that the effects of coupling may be relatively small in certain materials and it is assumed that electromechanical effects can be treated as a perturbation on the uncoupled solution. 

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. 

From a constitutive relation of the form t = t(D, ri) (here t is stress not time) it can be readily shown that, since there is no change in electric displacement in an open-circuit, thick-sample configuration, there are no secondary stresses due to electromechanical coupling. Nevertheless, the wavespeed is that of a piezoelectrically stiffened wave. 

Fig. 4.3. Typical normalized piezoelectric current-versus-time responses are compared for x-cut quartz, z-cut lithium niobate, and y-cut lithium niobate. The y-cut response is distorted in time due to propagation of both longitudinal and shear components. In the other crystals, the increases of current in time can be described with finite strain, dielectric constant change, and electromechanical coupling as predicted by theory (after Davison and Graham [79D01]).

From the mechanical viewpoint, ferroelectrics exhibit unsteady, evolving waves at low stresses. Waves typical of well defined mechanical yielding are not observed. Such behavior is sensitive to the electrical boundary conditions, indicating that electromechanical coupling has a strong influence. Without representative mechanical behavior, it is not possible to quantitatively define the stress and volume compression states exciting a particular electrical response. 

Studies of the electrical and mechanical responses of ferroelectric solids under shock compression show this technical problem to be the most complex of any investigated. The combination of rate-dependent mechanical and electrical processes along with strong electromechanical coupling has clouded physical interpretation of the numerous investigations. 

Ryanodine receptors are also localized to both the peripheral and central SR (Fig. 4) in smooth muscle (Lesh et al 1993), and extensive evidence indicates that caffeine releases Ca2+ through ryanodine receptors in smooth muscles, just as in striated muscle (reviewed in lino 2000). Ca2+ influx can also induce Ca2+ release from the SR in smooth muscle (Ganitkevich Isenberg 1995, Kamishima McCarron 1997), suggesting that Ca2+-induced Ca2+ release (CICR) is at least one of the mechanisms, first shown in cardiac muscle (Fabiato 1983), of electromechanical coupling in smooth muscle. 

Neuromuscular transmission (B) of motor nerve impulses to the striated muscle fiber takes place at the motor endplate. The nerve impulse liberates acetylcholine (ACh) from the axon terminal. ACh binds to nicotinic cholinocep-tors at the motor endplate. Activation of these receptors causes depolarization of the endplate, from which a propagated action potential (AP) is elicited in the surrounding sarcolemma. The AP triggers a release of Ca from its storage organelles, the sarcoplasmic reticulum (SR), within the muscle fiber the rise in Ca concentration induces a contraction of the myofilaments (electromechanical coupling). Meanwhile, ACh is hydrolyzed by acetylcholinesterase (p. 100) excitation of the endplate subsides. if no AP follows, Ca + is taken up again by the SR and the myofilaments relax. 

Dantrolene interferes with electromechanical coupling in the muscle cell by inhibiting Ca + release from the SR. It is used to treat painful muscle spasms attending spinal diseases and skeletal muscle disorders involving excessive release of Ca + (malignant hyperthermia). 

Probably the best measure of the effectiveness of a piezoelectric material is its electromechanical coupling constant, k, defined as... 

A special coupling between extracellular Ca influx and the ryanodin receptor exists in muscle cells. There, a voltage-dependent Ca channel, the dihydropyridine receptor, is coupled directly to the cytoplasmic domain of the ryanodin receptor (see Fig. 6.7a). A depolarization of the cell membrane is transmitted in this system via an electromechanical coupling directly to the gating state of the ryanodin receptor. 

Reinecke H, MacDonald GH, Hauschka SD, Murry CE. Electromechanical coupling between skeletal and cardiac muscle. Implications for infarct repair. J Cell Biol 2000 149(3) 73 I -740. 

The electromechanical coupling coefficient (k) is a measure of the ability of a piezoelectric material to transform mechanical energy into electrical energy, and vice versa. It is defined [5] by... 

IRE Standards on Piezoelectric Crystals determination of the elastic, piezoelectric and dielectric constants - the Electromechanical Coupling Factor, 1958, Proceedings IRE April 1958, 764-78. 

Table 1.1. Abundance of the metal in the earths s crust, optical band gap Es (d direct i indirect) [23,24], crystal structure and lattice parameters a and c [23,24], density, thermal conductivity k, thermal expansion coefficient at room temperature a [25-27], piezoelectric stress ea, e3i, eis and strain d33, dn, dig coefficients [28], electromechanical coupling factors IC33, ksi, fcis [29], static e(0) and optical e(oo) dielectric constants [23,30,31] (see also Sect. 3.3, Table 3.3), melting temperature of the compound Tm and of the metal Tm(metal), temperature Tvp at which the metal has a vapor pressure of 10 3 Pa, heat of formation AH per formula unit [32] of zinc oxide in comparison to other TCOs and to silicon...

Maggi CA, Giuliani S, Santicioli P (1995) CGRP inhibits electromechanical coupling in the guinea pig isolated renal pelvis. Naunyn-Schmiedeberg s Arch Pharmacol 352 529-537... 

Santicioli P, Maggi CA (1997) Pharmacological modulation of electromechanical coupling in the proximal and distal regions of the guinea pig pelvis. J Auton Pharmacol 17 43-52... 

The stiffness parameter C55 has, in effect, been increased by the factor (1 + K ) — an effect known as piezoelectric stiffening. The factor is the electromechanical coupling coefficient for the jt-propagating, z-polarized plane wave ... 

The last term is approximately equal to K when <4 1. Thus, the electromechanical coupling coefficient K ) has a second interpretation is approx-... 

---