Elasticity orientation dependence

Flow processes iaside the spinneret are governed by shear viscosity and shear rate. PET is a non-Newtonian elastic fluid. Spinning filament tension and molecular orientation depend on polymer temperature and viscosity, spinneret capillary diameter and length, spin speed, rate of filament cooling, inertia, and air drag (69,70). These variables combine to attenuate the fiber and orient and sometimes crystallize the molecular chains (71). 

Fig. 13 Schematic representation of the orientation-dependent elastic torque on a nickel nanowire with longitudinal anchoring in 5CB (a) in equilibrium, and (b) in the presence of a magnetic field, (c) Levitation of the nanowire in a twisted nematic cell [446]. (Copyright 2004, American Association for the Advancement of Science)...

For cubic symmetry materials, three independent elastic properties that are orientation dependent are required to describe the mechanical behavior of the material. This anisotropy effect increases significantly the number of the nonzero elements in the FE stiffness matrix leading to alteration in the calculated stress components and the wave speed. In order to test these anisotropy effects, we plot the wave profiles of three different orientations and compare it with the isotropic behavior with a loading axis in the [001] directions as shown in Fig 8. We observed that under the same loading condition, the peak stress of [111] and [Oil] orientations are slightly higher than those of the [001] which is lower that that of isotropic material. Furthermore, wave speed varies moderately with orientation with the fastest moving wave in the [ 111 ] followed by [011 ], isotropic medium and [001 ] respectively. 

Measurements of physical properties usually encompass the whole, undisturbed sediment. Two types of parameters can be distinguished (1) bulk parameters and (2) acoustic and elastic parameters. Bulk parameters only depend on the relative amount of solid and fluid components within a defined sample volume. They can be approximated by a simple volume-oriented model (Fig. 2.2a). Examples are the wet bulk density and porosity. In contrast, acoustic and elastic parameters depend on the relative amount of solid and fluid components and on the sediment frame including arrangement, shape and grain size distribution of the solid particles. Viscoelastic wave propagation models simulate these complicated structures, take the elasticity of the frame into account and consider interactions between solid and fluid constituents. (Fig. 2.2b). Examples are the velocity and attenuation of P-and S-waves. Closely related parameters which mainly depend on the distribution and capillarity of the pore space are the permeability and electrical resistivity. 

Recently, ten Bosch, Sixou and coworkers have extended theories for low molar mass nematic liquid crystals to cover aspects of the phase separation of semiflexible polymers (41-43). The polymer is taken to be an elastic worm-like chain with orientation dependent Van der Waals interactions. These theories have been applied to the phase separation of (hydroxypropyl)cellulose -dimethyl acetamide mesophases (17). 

The elastic constants depend on the product of the order parameters of two neighboring molecules. If one of the molecules had the order of 0, the second molecule can orient along any direction with the same inter-molecular interaction energy even if it has non-zero order parameter. Therefore the elastic constants are proportional to S. When the temperature changes, the order parameter will change and so will the elastic constants. 

Because of the a(hcp) structure of titanium, elastic properties depend on the orientation of the titanium crysteds and the texture of polycrystalline titanium. Interstitial impiuities (e.g. oxygen... 

Most properties are strongly influenced by chain orientation. Birefringence, thermal expansivity, thermal conductivity and the elastic modulus depend on the Hermans orientation function according to relatively simple formulae. However, the elastic modulus of ultra-oriented polymers depends more directly on the macroscopic and molecular draw ratio. The latter reflects the extension of the end-to-end vector and the axial chain continuity. 

Elasticity is a macroscopic property of matter defined as the ratio of an applied static stress (force per unit area) to the strain or deformation produced in the material the dynamic response of a material to stress is determined by its viscosity. In this section we give a simplified formulation of the theory of torsional elasticity and how it applies to liquid crystals. The elastic properties of liquid crystals are perhaps their most characteristic feature, since the response to torsional stress is directly related to the orientational anisotropy of the material. An important aspect of elastic properties is that they depend on intermolecular interactions, and for liquid crystals the elastic constants depend on the two fundamental structural features of these mesophases anisotropy and orientational order. The dependence of torsional elastic constants on intermolecular interactions is explained, and some models which enable elastic constants to be related to molecular properties are described. The important area of field-induced elastic deformations is introduced, since these are the basis for most electro-optic liquid crystal display devices. 

The orientation dependence of the elastic moduli changes with the intermetallic compound, although it has a common trend for single crystals with a tetragonal structure, as shown in Figure 2. 

The atomic arrays of intermetallic compounds may affect the orientation dependence of the elastic constants. Table 4 shows the ratio of the interatomic distance in the [ijk] direction to that in the [001] direction, and the associated stiffness-constant and compliance-constant ratios for various intermetallics (Nakamura, 1991a). Here, andS[j, t] represent c,... 

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