Deformation, bending-twisting

Backbone fractal dimension 54 Bending-twisting deformation 55 BET-surface area 13-14, 20 Brake system, frictional 145 Breakdown, filler cluster 64, 76... 

In addition to the descriptions of group vibrations as stretch and bend (or deformation) the terms rock, twist, scissors, wag, torsion, ring breathing and inversion (or umbrella) are used frequently these motions are illustrated in Figure 6.13. 

Fig. 6. The three basic curvature deformations of a nematic Hquid crystal bend, twist, and splay. The force constants opposing each of these strains are...

FIGURE 22.9 Schematic view demonstrating the mechanical equivalence between a Hller cluster and a series of soft and stiff molecular springs, representing bending-twisting and tension deformation of filler-filler bonds, respectively. (From Kluppel, M. and Heinrich, G., Kautschuk, Gummi, Kunststojfe, 58, 217, 2005. With permission.)... 

It has been shown 65,68) that the threshold voltage is a function of the dielectric anisotropy Ae and the elastic constants of splay (ku), twist (k22) and bend (k33) deformation of the nematic phase (Fig. 17) ... 

Here, kb=Q/d2 is the force constant of longitudinal deformations of filler-filler bonds and ks is the bending-twisting force constant of the cluster, which is given by Eq. (28). From Eq. (31) one finds that the yield strain of a... 

The three kinds of deformations are associated with the variation of n, i.e. Vn. For the splay deformation, the divergence of the n vectors, V n, is not zero for the twist deformation, n V x n 0, and for the bend deformation, n x V x n 0. In order to describe the meaning of the three formulae, it is supposed that in the undeformed sample, n points along the z direction. These three deformations can hence be written in the form of components as follows... 

It is noted that there is no twisted deformation in liquid crystals, thus the K22 term does not appear in Fs. If the deformation is not so great, the splay deformation is dominant. When the deformation becomes greater, the bend deformation becomes more important. 

Here nd are elastic constants. The first, is associated with a splay deformation, K2 is associated with a twist deformation and with bend (figure C2.2.11). These three elastic constants are termed the Frank elastic constants of a nematic phase. Since they control the variation of the director orientation, they influence the scattering of light by a nematic and so can be determined from light-scattering experiments. Other techniques exploit electric or magnetic field-induced transitions in well-defined geometries (Freedericksz transitions, see section (C2.2.4.1I [20, M]. 

Stresses, due to tectonic activity, within the Earth s crust create subject rocks to bend, twist or fracture and consequently deform giving rise to rock bodies undergoing transformation in position, alignment, orientation and form. A working knowledge of subsurface rock structures is essential for engineering practice. 

---