Experimental elastic properties

The role of yeast in fermenting dough maturation is even less clear. The alcohol and carbon dioxide developed during fermentation must influence the elastic properties of the protein matrix. However, experimental procedures that would permit this to be checked in the absence of yeast have not been developed. 

The Debye temperature, can be calculated from the elastic properties of the solid. Required are the molecular weight, molar volume, compressibility, and Poisson s ratio.11 More commonly, do is obtained from a fit of experimental heat capacity results to the Debye equation as shown above. Representative values for 9o are as follows ... 

Typically, the insertion induces sharp variation of the membrane profile at the distances 0.5-1.0nm from the membrane-peptide interface [79-82]. The steepness of this perturbation indicates that the short-A, behavior of membrane moduli must be important in the estimates of the elastic energy. In addition, a peptide inserted in a membrane almost certainly perturbs the membrane s elastic moduli in the immediate vicinity of the inclusion. Both these effects, membrane nonlocality and nonuniform modification of elastic properties by insertions, might play an important role in resolving the contradiction between the local calculations [80] and the experimental data for the mean lifetime of a gramicidin channel [81,109,110]. ... 

More recently, Smith et al. have developed another model based on spontaneous curvature.163 Their analysis is motivated by a remarkable experimental study of the elastic properties of individual helical ribbons formed in model biles. As mentioned in Section 5.2, they measure the change in pitch angle and radius for helical ribbons stretched between a rigid rod and a movable cantilever. They find that the results are inconsistent with the following set of three assumptions (a) The helix is in equilibrium, so that the number of helical turns between the contacts is free to relax, (b) The tilt direction is uniform, as will be discussed below in Section 6.3. (c) The free energy is given by the chiral model of Eq. (5). For that reason, they eliminate assumption (c) and consider an alternative model in which the curvature is favored not by a chiral asymmetry but by an asymmetry between the two sides of the bilayer membrane, that is, by a spontaneous curvature of the bilayer. With this assumption, they are able to explain the measurements of elastic properties. 

Calculations of the elastic properties, the main tensions and tensile strength of natural rubber carried out without using the empirical adjusting parameters are in good agreement with the experimental data. 

The relaxation spectrum H is independent of the experimental time t and is a fundamental description of the system. The exponential function depends upon both the experimental time and the relaxation time. Such a function in the context of this integral is called the kernel. In order to describe different experiments in terms of a relaxation spectrum H or retardation spectrum L it is the kernel that changes. The integral can be formed in time or frequency depending upon the experiment being modelled. The inclusion of elastic properties at all frequencies and times can be achieved by including an additional process in the relaxation... 

For coarse-grained models of linear biopolymers—such as DNA or chromatin— two types of interactions play a role. The connectivity of the chain implies stretching, bending, and torsional potentials, which exist only between directly adjacent subunits and are harmonic for small deviations from equilibrium. As mentioned above, these potentials can be directly derived from the experimentally known persistence length or by directly measuring bulk elastic properties of the chain. 

Three-dimensional distributions of the micro-residual stresses are very complicated, and are affected by the elastic properties, local geometry and distribution of the composite constituents within a ply. Many analytical (Daniel and Durelli, 1962 Schapery, 1968 Harris, 1978 Chapman et ah, 1990 Bowles and Griffin, 1991a, b Sideridis, 1994) and experimental (Marloff and Daniel, 1969 Koufopoulos and Theocaris, 1969 Barnes et ah, 1991 Barnes and Byerly, 1994) studies have been performed on residual thermal stresses, A two-dimensional photoelastic study identified that the sign and level of the residual stresses are not uniform within the composite, but are largely dependent on the location (Koufopoulos and Theocaris,... 

Mention should be made in this connection of the physics and chemistry involved in faulting as well as in jointing and minor movements of the solid rocks. These phenomena have often been treated under the principles of elastic theory as applied to homogeneous bodies, yet there can be no question that the elastic properties and conditions of rupture of aggregates must differ in many essential particulars from those of homogeneous bodies. Here is a considerable field for experimentation. 

Figure 13.5(d) presents experimental stiffness measurements using differential UFM for three high modulus surfaces sapphire, Si(100) and LiF(lOO) (Dinelli et al. 2000b). The samples were probed with the same silicon tip on a V-shaped cantilever (nominally cantilever stiffness was kc - 2.8 nN nm 1,and radius of curvature R = 10 nm). The surface RMS roughness of the surfaces was less than 0.2 nm over a few square micrometres for all three samples. The relative difference between the three sets of data reveals that the elastic properties of these three materials can be distinguished by differential UFM the relative independence of the applied force may indicate the fact that the tip had been flattened by extended contact with such hard samples. 

In spite of their long history, reinforcement mechanisms and elastic properties of elastomers remain the subject of numerous experimental investigations 111 116>, but... 

An examination of the experimental findings and the calculation model shows that the deformability of a syntactic foam depends mainly on the elastic properties of the polymer matrix, whereas the filler concentration mainly affects its compressibility. In fact, monolithic (unfilled) samples do deform elastically at the start of the compression curve, but when the material is deformed further, the forced elasticity limit is reached (Fig. 21). Thus, the nominal ultimate strength for non-brittle failure is determined by the fact that the forced elastic limit is reached, and not because the adhesive ties have lost their stability (as it is the case with light plastic foams) 8 10). 

In addition to strength and WOF of FMs, the elastic behavior of these architectures should be considered. Simple brick models were proposed to accurately predict elastic properties of FMs [1, 24], Figure 1.8 shows the elastic modulus versus orientation for uniaxially aligned Si3N4/BN FMs with experimentally measured values, indicating that there is very good agreement between experiment and prediction. This prediction can be used for FMs with multiaxial architectures. 

Note that the residual stress aM — 0 on the elastic properties becomes homogeneous (Ef = Em = EL). While connections between the residual stresses and constituent properties are rigorous, experimental determination is still necessary, because ft is not readily predictable. In general, ft includes terms associated with the thermal expansion difference, ay— am, as well as volume changes that occur either upon crystallization or during phase transformations. For CVI systems, intrinsic stresses may also be present. 

The elastic properties discussed so far relate to stresses applied at relatively low rates. When forces are applied at rapid rates, then dynamic moduli are obtained. The energy relationships and the orders of magnitude of the data are much different [570]. Because of the experimental difficulties, only little work at rapid rates has been carried out with cotton fiber compared to that done with testing at low rates of application of stress. In contrast, cotton also responds to zero rate of loading, i.e., the application of a constant stress. Under this condition the fiber exhibits creep that is measured by determining fiber elongation at various intervals of time after the load has been applied. Creep is time-dependent and may be reversible upon removal of the load. However, even a low load applied to a fiber for a long period of time will cause the fiber to break. 

Figure 10.2. Experimental set-up used to study the elastic properties of thin films by RUS. The resonance frequencies are measured with the piezoelectric tripod. The scanning laser-Doppler interferometer draws the oscillation displacement of specimen surface. (Reproduced with permission of Elsevier, Ref. [22].)...

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