Elasticity direction dependence

Mechanical Behavior of Materials. Different kinds of materials respond differently when they undergo basic mechanical tests. This is illustrated in Eigure 15, which shows stress—strain diagrams for purely viscous and purely elastic materials. With the former, the stress is reheved by viscous flow and is independent of strain. With the latter, there is a direct dependence of stress on strain and the ratio of the two is the modulus E (or G). 

The energy which drives the fragmentation process (elastic plus kinetic) is determined by the dynamic loading conditions and does not directly depend on the properties of the material at issue. The fragmentation energy, on the other hand, is an intimate property of the material and can depend in a complex way on the thermal and dynamic conditions at spall, as well as on the deformation history of the material leading to spall. 

Therefore, switch-off times are independent of the field strength and directly dependent on material parameters, such as viscosity coefficients and elastic constants, and the cell configuration. Therefore, they are often three or four orders of magnitude larger than the switch-on times. However, sophisticated addressing techniques can produce much shorter combined response times ( on + off The nematic director should be inclined, e.g. 1° pretilt,... 

In Sect. 3.2 the preparation of magnetic polymer composites under uniform magnetic field has been described. The resulting composites show anisotropic behavior. The anisotropy manifests itself in the direction-dependent elastic modulus. Figure 13 shows carbonyl iron-loaded mPDMS elastomers. All three samples contain the same amount of filler particles, but the spatial distribution of the filler is different, as shown in the figure. 

The experimental data were analyzed on the basis of Eq. 7. It is seen that the slopes of the straight lines (elastic moduli, G) are direction-dependent. The elastic modulus is larger if the compression force and the direction of pearl chain structure are parallel. This finding indicates a strong mechanical anisotropy. It can be concluded that the spatial distribution of the solid particles has a decisive effect on the stress-strain dependence. 

This elastic scattering term is known as the elastic incoherent structure factor. It decreases from unity at (2 = 0 to 0 at large Q. As the area of S" (Q, (o) in the 00 direction is unity, there is an additional quasi-elastic component that increases from 0 at (2 = 0 to unity at large Q. The form of the quasi-elastic component depends on the nature of the localised diffusion. In the simplest case, where the jumping is between two trapping sites, the quasi-elastic term is a Lorentzian with a (2-independent width which is just 1/t where x is the mean residence time on either site. Two specific models will be noted here (a) random jumping round a ring of sites, the Barnes model [38] and (b)... 

The cutting process begins with elastic deformation upon contact of the cutting edge. While penetration as well as forces in the contact zone increase, the material becomes plastic but will only be displaced. The displacement vectors of different material elements are directed into different directions, depending on where in the... 

For anisotropic materials, there are more elastic constants, depending on the direction of test. For example, for uniaxially aligned chains or fibres, with which this chapter is mostly concerned, there are two overall or macroscopic values of E and Ex if th sample has transverse... 

In order to effectively assess the variation of the directionally dependent elastic modulus, the results were normalised relative to elastic modulus along Y direction, i.e. = Ej/E2 (i=l, 2 and 3), as shown in Figure 11. The comparison and difference can be more readily seen with normalised average values added. The degree of anisotropy (DA) is thus be calculated and plotted for each sintering temperature DA=l-smallest normalised modulus, with DA=0 when fliUy isotropic and DA=1, fully anisotropic. 

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. 

By maintaining constant the vessel section and modifying the height of liquid column, a direct dependence of the chemo-acoustic degradation and degradation parameters, as effect of the different distribution of the elastic energy in the reaction medium [1112]. 

Table 2.3 contains an overview of the elastic constants for some metals and ceramics. As can be seen, the anisotropy factor of tungsten is 1.0, so it is (almost) isotropic even as a single crystal. For most other materials, almost isotropic properties can only be found in a polycrystalline state. The direction dependence of Young s modulus for selected materials is plotted in figure 2.10. 

The structural anisotropy manifests itself in both direction dependent elastic modulus and direction dependent swelling. To demonstrate the direction dependent elastic modulus, stress-strain measurements were performed. The elastic modulus was determined by unidirectional compression... 

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