Total true strain

For very small (infinitesimal) strains, this is identical to the nominal strain. To calculate the total true strain y>, the increments dip have to be integrated ... 

Figure 7.11. True stress-strain curve for aorta. Total, elastic, and viscous stress-strain curves for aorta. The total stress-strain curves (open boxes, top) were obtained by collecting all the initial, instantaneous, force measurements at increasing time intervals and then dividing by the initial cross-sectional areas and multiplying by 1.0 + the strain. The elastic stress-strain curves (closed diamonds, middle) were obtained by collecting all the force measurements at equilibrium and then dividing by the initial cross-sectional areas and multiplying by 1.0 + the strain. The viscous component curves (closed squares, bottom) were obtained as the difference between the total and the elastic stresses. Error bars represent one standard deviation of the mean.

Figure 19.22 Total energy density versus applied true strain for cyclic tension. (From Reference 10 with permission from Elsevier Inc.)...

Fig. 3.1. Comparison of nominal and true strain for a deformation of a tensile specimen in one or two steps, respectively. In total, the length is doubled during the deformation. The nominal strain differs (si + 2 / 12) while the true strain is identical (< i + < 2 = >12) for both deformation sequences...

A subtraction of the total amount of stress decay, Aazz(t oo), from the respective initial stresses measmed along the stretching curve gives the stress-true strain relationship associated with the limit of zero strain rates, i.e., under quasi-state conditions. The quasi-static stress-strain relationship obtained in this manner for PEVA12 is included in Fig. 10.5. 

Note that the so-called thermal forces, N, are true thermal forces only when the total strains and curvatures are perfectly restrained, that is, zero. 

This stress is to be accounted for when computing the total stress in the sub wall. The calculation can be done easily in real time with a computer however, it is easier and probably more accurate to measure a difference in strain (or stress) in the sub between the off-bottom position and while drilling. This value should be related closely to the true weight-on-bit. 

The basis for the above-mentioned model47) was provided by Maxwell s nonlinear model obtained in general form in Ref. 48). Flere the total strain was divided into irreversible strain and elastic strain X, Stress a and velocity of irreversible strain ep were determined from the elastic strain. In Ref. 48) a number of functions a (a.) and ep(X) were defined more specifically. Beside that, Maxwell s nonlinear models were connected in parallel. Note that in case of one Maxwell s element X = a23), but in case of several elements connected in parallel this is not true and a is determined from the solution of the respective problem. In case of the uniaxial extension the model of Ref.47) takes the following form ... 

If we accept the premise that the total strain is a key variable in the quality of laminar mixing, we are immediately faced with the problem that in most industrial mixers, and in processing equipment in general, different fluid particles experience different strains. This is true for both batch and continuous mixers. In the former, the different strain histories are due to the different paths the fluid particles follow in the mixer, whereas in a continuous mixer, superimposed on the different paths there is also a different residence time for every fluid particle in the mixer. To quantitatively describe the various strain histories, strain distribution functions (SDF) were defined (56), which are similar in concept to the residence time distribution functions discussed earlier. 

In principle, directed evolution procedures could be repeated indefinitely until any desired activity has been attained. At some point, however, the catalyst will be sufficiently active that the host cell grows like the wild-type strain, making selection for further improvement difficult. This is true for the modified hexamer even though it is still an order of magnitude less efficient than the homodimeric MjCM [37]. Since total activity depends on the catalyst concentration as well as specific activity, reducing the available catalyst concentration can further increase selection pressure. In practice, intracellular protein concentrations can be lowered in a variety of ways, including the use of low copy plasmids [101], weak promoters [102] and inefficient ribosome binding sites [103]. 

N. CABRERA (University of Virginia) I do not agree that the strain energy of a screw dislocation does not necessarily influence the process of dissolution. It is true that a screw dislocation has no strain energy at the surface however, it is the change in the total energy of the crystal that must be considered... 

Figure 1-2 records some typical stress-strain curves for different polymer types. Some polymers exhibit a yield maximum in the nominal stress, as shown in part (c) of this figure. At stresses lower than the yield value, the sample deforms homogeneously. It begins to neck down at the yield stress, however, as sketched in Fig. 11-20. The necked region in some polymers stabilizes at a particular reduced diameter, and deformation continues at a more or less constant nominal stress until the neck has propagated across the whole gauge length. The cross-section of the necking portion of the specimen decreases with increasing extension, so the true stress may be increasing while the total force and the nominal stress...

Some further consideration reveals that this analysis is also true if the sample consists of many crystals which disporportionate instead of just a single crystal. Hence, in a normal sample, the disproportionation can be made without a change in the total surface area, number of CS planes, or number of crystals. The net change in elastic-strain energy is then given by [(17s)" ... 

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