Elastic constants compression

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]. 

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). 

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... 

The problem of definition of modulus applies to all tests. However there is a second problem which applies to those tests where the state of stress (or strain) is not uniform across the material cross-section during the test (i.e. to all beam tests and all torsion tests - except those for thin walled cylinders). In the derivation of the equations to determine moduli it is assumed that the relation between stress and strain is the same everywhere, this is no longer true for a non-linear material. In the beam test one half of the beam is in tension and one half in compression with maximum strains on the surfaces, so that there will be different relations between stress and strain depending on the distance from the neutral plane. For the torsion experiments the strain is zero at the centre of the specimen and increases toward the outside, thus there will be different torque-shear modulus relations for each thin cylindrical shell. Unless the precise variation of all the elastic constants with strain is known it will not be possible to obtain reliable values from beam tests or torsion tests (except for thin walled cylinders). 

A Theoretical Investigation into Some Properties of Ionic Crystals. A Quantum Mechanical Treatment of the Cohesive energy, the Interionic Distance, the Elastic Constants, and the Compression at High Pressures with Numerical Ap-... 

The dilational rheology behavior of polymer monolayers is a very interesting aspect. If a polymer film is viewed as a macroscopy continuum medium, several types of motion are possible [96], As it has been explained by Monroy et al. [59], it is possible to distinguish two main types capillary (or out of plane) and dilational (or in plane) [59,60,97], The first one is a shear deformation, while for the second one there are both a compression - dilatation motion and a shear motion. Since dissipative effects do exist within the film, each of the motions consists of elastic and viscous components. The elastic constant for the capillary motion is the surface tension y, while for the second it is the dilatation elasticity e. The latter modulus depends upon the stress applied to the monolayer. For a uniaxial stress (as it is the case for capillary waves or for compression in a single barrier Langmuir trough) the dilatational modulus is the sum of the compression and shear moduli [98]... 

Using elastic constants a relation was given with in-plane compressive stress cr > 0 (TABLE 4). 

Also the curvature of the loading curve is an indication of the presence of a compressible material. The third curve in Fig. 29 can be fitted with a function in the form F=F0+az2 without any linear term, whereas the second curve can be fitted with a linear term. This means that, when the tip is placed on the residues of the border walls inside the rectangles, it pushes at the beginning on a soft material that becomes stiffer and stiffer as the tip compresses it. Consequently, the slope of the loading curve goes from 0 (very soft material) to kc, i.e. the elastic constant of the cantilever (very stiff material). 

The complexity of N205 and the absence of compressibility or elastic constant data preclude any reliable calculation of the nonelectrostatic... 

In the zincblende structure, with three independent elastic constants, the use of a model with only two parameters will allow a test and also allows alternate ways of obtaining the parameters. We obtain the radial force constant from a uniform compression, e, = = Cj = r, from which we obtain a change in energy per bond... 

When the full expression (21) will be determined, say, from the experimental second virial coefficient it will be possible to calculate all constants (compressibility, elastic constants, etc.) of these molecular lattices. 

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