Shape deformation

Fig. 2. The shape-memory process, where Tis temperature, (a) The cycle where the parent phase undergoes a self-accommodating martensite transformation on cooling to the 24 variants of martensite. No macroscopic shape change occurs. The variants coalesce under stress to a single martensite variant, resulting in deformation. Then, upon heating, they revert back to the original austenite crystallographic orientation, and reverse transformation, undergoing complete recovery to complete the cycle, (b) Shape deformation. Strain recovery is typically ca 7%.

In the past when car crashworthiness was designed entirely experimentally, full-sized prototypes were subjected to the crash scenarios required by the relevant authorities. If the performance was unacceptable, the shape deformations of the components making up the prototype were examined. A new prototype was engineered empirically to overcome the identified weaknesses before being built and then destroyed in a subsequent test. These tests would be repeated many times before an appropriate design was found. The cost of the process was enormous. 

The above short list does not offer a hint about the sign of the effect. All of the cavities including ours are of special types i.e., the angles are fixed. Thus we still do not know about the dependence on the shape deformations. 

Drops accelerated by an air stream may split, as described in Chapter 12. For drops which do not split, measured drag coefficients are larger than for rigid spheres under steady-state conditions (R2). The difference is probably associated more with shape deformations than with the history and added mass effects discussed above. For micron-size drops where there is no significant deformation, trajectories may be calculated using steady-state drag coefficients (SI). 

Martensitic transformations involve a shape deformation that is an invariant-plane strain (simple shear plus a strain normal to the plane of shear). The elastic coherency-strain energy associated with the shape change is often minimized if the martensite forms as thin plates lying in the plane of shear. Such a morphology can be approximated by an oblate spheroid with semiaxes (r, r, c), with r c. The volume V and surface area S for an oblate spheroid are given by the relations... 

If S is the lattice-invariant deformation tensor and R the rigid-body rotation tensor, the total shape deformation tensor, E, producing the invariant plane can be expressed as... 

Furthermore, Fujiwara et al. (2004a) performed an experimental study using PIV/LIF combining with double-SIT to construct approximated 3D shape deformation of bubbles as well as to investigate quantitatively the 3D wake flow structures behind bubbles in a simple shear flow. The... 

A given material may be a solid under some conditions and a liquid under others for example a plastic material is a solid at stresses lower than its yield stress but a liquid at higher stresses. The term semi-solid is a convenient, though imprecise, description of materials that when unsupported by a container, change shape (deform) under the influence of gravity under ambient conditions. Many fat-based foods are semi-solid. 

Figure 6. Electron micrograph illustrating V-shaped deformation bands within the hydrogen-bonded (010) planes of fractured nylon 66, Micron marker insert, an edge view of fracture surface running from (010) plane through the thin direction of the strip (Figure 2),...

At 24 h after the start of the release the plume maximum had spht into two separate parts (Fig. 5.2). The head received cyclonic rotational momentum from a meso-scale disturbance and reached DK02 after 26 h giving rise to the first peak. As the latter part of the cloud progressed it received anti-cyclonic momentum and after 36 h the plume attained a U-shaped deformation which was advected towards DK02. The rotational time scale of the eddies was not large enough (compared to the advective time scale of the plume) to cause a full revolution in the plume. 

In general, the change in volume caused by the field E consists of an isotropic contribution AF and an anisotropic one AF f ". The latter is chiefly due to shape deformation of the dielectric sample. In fact, it should be stated that an isotropic body can exhibit anisotropic electrostriction, accorfhng to the method adopted by the experimenter this eventuality should be eliminated as far as possible in measurements. The constant given by (164b) is non-zero only if the electrostriction apparent in the macroscopic medium is anisotropic. Anisotropy of electrostriction can to some degree affect the measurement of the Kerr constant but if the necessary precautions are taken, the part due to is eliminated completely or at least made quite insignificant. 

Closer study of the absorption band shifted by stress showed a shape deformation which could be interpreted as a non-uniform stress distribution i.e. some bonds are more highly stressed than others and consequently suffer a higher-than-average frequency shift. Such bonds were designated over-stressed bonds and their distribution with respect to stress was deduced. An example is shown in Fig. 5 for... 

In fact, F is also required to be at a minimum with respect to all possible membrane deformations, and this minimization with respect to membrane shape must be carried out self-consistently together with the electrostatic and lipid mixing contributions [27,36]. This presents a challenge, since in principle one has to consider all possible variations in membrane geometry, and these multiple shape deformations generally couple to other degrees of freedom. 

While vesicle deformation in AC fields concerns stationary shapes, DC pulses induce short-lived shape deformations. In different studies, the pulse duration has been typically varied from several microseconds to milliseconds, while studies on cells have investigated a much wider range of pulse durations-from tens of nanoseconds to milliseconds and even seconds [80], as discussed in other chapters of this book. Various pulse profiles, unipolar or bipolar, as well as trains of pulses have been also employed (e.g., [81, 82]). Because the application of both AC flelds and DC pulses creates a transmembrane potential, vesicle deformations of similar nature are to be expected in both cases. However, the working fleld strength for DC pulses is usually higher by several orders of magnitude. Thus, the degree of deformation can be different. 

In the case of predominant van der Waals attfaction, instead of a dimple, a reverse bell-shaped deformation, called a pimple, appears and the film quickly ruptures. 4 5,472,48i,484 jjjg thickness, hp, at which the pimple appears can be calculated from the relationship ... 

Calculations for larger drops are complicated by phenomena such as shape deformation, wake oscillations, and eddy shedding, making theoretical estimates of E difficult. The overall process of rain formation is further complicated by the fact that drops on collision trajectories may not coalesce but bounce off each other. The principal barrier to coalescence is the cushion of air between the two drops that must be drained before they can come into contact. An empirical coalescence efficiency Ec suggested by Whelpdale and List (1971) to address droplet bounce-off is... 

The comparison of the two figures shows that the characteristic bubble frequency for ground conditions is two times smaller than that for microgravity conditions. The most probable reason for the decrease of the characteristic bubble frequency under ground conditions is the bubble shape deformation due to gravity on which the characteristic frequency strongly depends. 

In the present extrusion of HDPE ribbons, the deformation patterns were examined by the deformation of parallel ink marks preimprinted on the surface of a HDPE (Figure 1-d). At EDR >12, the low and high MW HDPE exhibited a typical shear parabola and a W-shape deformation profile, respectively, with both characteristics enhanced at higher EDR as shown in Figure 2. These characteristics of the deformation patterns are in well agreement with our previous observations (3) and further confirm the previous conclusion that there is no significant effect of cutting a billet into two halves and/or coextrusion of a film with the split billet halves on the deformation flow patterns. 

Figure 8.16 The sequence of events taking place during the deformation and recovery of a shape using a shape-memory alloy. Cooling the high-temperature shape below Mf transforms it into a multiply twinned form with the same overall shape. Deformation alters the distribution of the twin boundaries. Reheating the sample above Af causes the material to revert to the high-temperature form. This removes the twins and allows the original shape to be recovered. The temperatures are appropriate to TiNi...

Some modes may dominate for example, for large bending strains in a flexible structure, fibre fracture in tension and fibre kinking in compression wdl dominate near both surfaces. Matrix cracks can cause delamination when they reach a ply interface. If the structure is stiff enough to resist with a significant force, then local indentation damage, and shear-driven delamination in the interior, wdl occur. Figure 9.2 shows schematically the different modes of fadure in three zones of a laminate. The peanut shape deformations (3) have this shape because the compression under the impact force suppresses the delaminations. 

Figure 3.29. (a) Photomechanical response of an LCE sample, (b) The shape deformation of an LCE sample upon exposure to light at A = 514 nm. (c) Mechanism of the locomotion of the dye-doped LCE sample. Source Camacho-Lopez et al., 2004. 

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