Elastic compressibility constant

The first term of Equation 8.4 comes from the dipole moment of the nanofiber web at constant thickness, which mainly depends on the number of effective dipoles (N ) present in the nanofiber web. The second term is known as the elastic compressibility constant (cry) directly related to the dimensional changes. One of the vital advantages of the nanofiber web-based pressure sensor or generator is that the expected piezoelectric effect is much higher due to the high compressibihty associated with the large thickness change at the identical pressure compared to its film form and to ceramic-based piezoelectric materials. 

To examine this peculiar behavior, we have converted the elastic compressibility modulus, per unit area, Y (Fig. 12a), to the modulus per chain, Y = F/10 F (Fig. 12b). The elastic compressibility modulus per chain is practically constant, 0.6 0.1 pN/chain, at high densities and jumps to another constant value, 4.4 0.7 pN/chain, when the density decreases below the critical value. The ionization degree, a, of the carboxylic acid determined by FTIR spectroscopy gradually decreases with increasing chain density due to the charge regulation mechanism (also plotted in Fig. 12b). This shows that a does not account for the abrupt change in the elastic compressibihty modulus. 

All these measures are applicable to monitor the development of the properties of the rock during loading and deformation. The development of the dilatancy can be divided very roughly into three phases. Phase I characterizes a decrease of the volume attributed to elastic compression of the rock salt, a decrease of permeability and an increase of seismic velocity. The volume becomes nearly constant at the end of Phase I. It can be assumed that elastic compression processes and dilatancy processes balance at this point. Dilatant microcracking generates only weak AE activity. 

The bulk modulus and the compressibility can be calculated by running molecular dynamics simulations to give equilibrium volumes at variable pressure. A simple method for the approximate calculation of the bulk modulus and of the elastic stiffness constants in the three main directions of a solid, using static simulation, will now be described, to illustrate how a macroscopic property like an elastic stiffness constant... 

Yet another technique, measuring ultrasonic velocity anisotropies in the vicinity of the NA transition, however, also find anisotropies consistent with crossover behaviour. Sonntag et al [52] studied the divergence of three elastic constants, the bulk compression constant A, the layer compression constant B and the bulk-layer coupling constant C. B and C have critical exponents that are unequal and are in between that of the 3DXY values and anisotropic scaling values. 

Here Fq is tire free energy of the isotropic phase. As usual, tire z direction is nonnal to tire layers. Thus, two elastic constants, B (compression) and (splay), are necessary to describe tire elasticity of a smectic phase [20,19, 86]. 

Wlrile quaternary layers and stmctures can be exactly lattice matched to tire InP substrate, strain is often used to alter tire gap or carrier transport properties. In Ga In s or Ga In Asj grown on InP, strain can be introduced by moving away from tire lattice-matched composition. In sufficiently tliin layers, strain is accommodated elastically, witliout any change in the in-plane lattice constant. In tliis material, strain can be eitlier compressive, witli tire lattice constant of tire layer trying to be larger tlian tliat of tire substrate, or tensile. 

Thermal Properties at Low Temperatures For sohds, the Debye model developed with the aid of statistical mechanics and quantum theoiy gives a satisfactoiy representation of the specific heat with temperature. Procedures for calculating values of d, ihe Debye characteristic temperature, using either elastic constants, the compressibility, the melting point, or the temperature dependence of the expansion coefficient are outlined by Barron (Cryogenic Systems, 2d ed., Oxford University Press, 1985, pp 24-29). 

When a foam is compressed, the stress-strain curve shows three regions (Fig. 25.9). At small strains the foam deforms in a linear-elastic way there is then a plateau of deformation at almost constant stress and finally there is a region of densification as the cell walls crush together. 

In the perfectly elastic, perfectly plastic models, the high pressure compressibility can be approximated from static high pressure experiments or from high-order elastic constant measurements. Based on an estimate of strength, the stress-volume relation under uniaxial strain conditions appropriate for shock compression can be constructed. Inversely, and more typically, strength corrections can be applied to shock data to remove the shear strength component. The stress-volume relation is composed of the isotropic (hydrostatic) stress to which a component of shear stress appropriate to the... 

Fig. 2.8. Idealized elastic/perfectly plastic solid behavior results in a stress tensor in which there is a constant offset between the hydrostatic (isotropic) loading and shock compression. Such behavior is only an approximation which may not be appropriate in many cases.

The piezoelectric constant studies are perhaps the most unique of the shock studies in the elastic range. The various investigations on quartz and lithium niobate represent perhaps the most detailed investigation ever conducted on shock-compressed matter. The direct measurement of the piezoelectric polarization at large strain has resulted in perhaps the most precise determinations of the linear constants for quartz and lithium niobate by any technique. The direct nature of the shock measurements is in sharp contrast to the ultrasonic studies in which the piezoelectric constants are determined indirectly as changes in wavespeed for various electrical boundary conditions. 

The mechanics of materials approach to the micromechanics of material stiffnesses is discussed in Section 3.2. There, simple approximations to the engineering constants E., E2, arid orthotropic material are introduced. In Section 3.3, the elasticity approach to the micromechanics of material stiffnesses is addressed. Bounding techniques, exact solutions, the concept of contiguity, and the Halpin-Tsai approximate equations are all examined. Next, the various approaches to prediction of stiffness are compared in Section 3.4 with experimental data for both particulate composite materials and fiber-reinforced composite materials. Parallel to the study of the micromechanics of material stiffnesses is the micromechanics of material strengths which is introduced in Section 3.5. There, mechanics of materials predictions of tensile and compressive strengths are described. 

The constant value of 0.25 for Poisson s ratio versus depth reflects the geology and the rock mechanics of the mature sedimentary basin in the West Texas region. Since mature basins are well cemented, the rock columns of West Texas will act as compressible, brittle, elastic materials. 

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