Experimental Force-Displacement Curves

EXPERIMENTAL FORCE-DISPLACEMENT CURVE FORCE FORCE prop FORCE UpropsO Fmax UpropasO... 

Figure 10.17. Typical smooth (top) and jagged (bottom) force-displacement curves created by averaging the forces of five curves and adding their oscillations multiple by Vs. Notice that the recreated ( typical ) curve is indistinguishable from the experimental ones. From Ulbricht et al. (1995).

The maximum radial stress as a function of the mechanical properties of the components and the geometry are calculated by finite-element modeling. The critical load must be determined experimentally. It may be observed by a kink in the force-displacement curve, by direct optical observation, or by acoustic emission analysis. The calculated stress concentration factors for different curvatures of the interface are given in Table 1. 

The most important validation of the model will be the comparison of the experimental and numerical force-displacement curves. If the numerical model is simulating the behavior of the knitted stmcture correctly, then the shapes of these curves should be very similar and the only difference should be the scale of force since the numerical simulation uses fewer filaments. Visual checks can also be used, e.g., comparison of loop height and width or wale/course density given as number of vertical/horizontal columns/rows of loops per cm for both the experimental and numerical case. 

Fig. 1. Schematic diagram illustrating the mechanical instability for (a) a weak spring (spring constant k) a distance D from the surface, experiencing an arbitrary surface force (after [19]) and (b) the experimentally observed force-distance curve relative to the AFM sample position (piezo displacement) for the same interaction.

Quantitative evaluation of a force-distance curve in the non-contact range represents a serious experimental problem, since most of the SFM systems give deflection of the cantilever versus the displacement of the sample, while the experimentalists wants to obtain the surface stress (force per unit contact area) versus tip-sample separation. A few prerequisites have to be met in order to convert deflection into stress and displacement into tip-sample separation. First, the point of primary tip-sample contact has to be determined to derive the separation from the measured deflection of the cantilever tip and the displacement of the cantilever base [382]. Second, the deflection can be converted into the force under assumption that the cantilever is a harmonic oscillator with a certain spring constant. Several methods have been developed for calibration of the spring constant [383,384]. Third, the shape of the probe apex as well as its chemical structure has to be characterised. Spherical colloidal particles of known radius (ca. 10 pm) and composition can be used as force probes because they provide more reliable and reproducible data compared to poorly defined SFM tips [385]. 

Comparison with Experimental Data The validity of the proposed analytical model for predicting the flexural response of R/C jacketed members was examined by comparing (i) for monotonic loading, the analytical lateral load versus lateral displacement curves along with the envelope experimental curves of the recorded lateral load versus lateral displacement hysteretic loops from various experimental studies (Thermou et al. 2007) (the monotonic moment-curvature response curves were derived according to the analytical model and then converted to force-displacement response curves). In Fig. 10, the experimental lateral load versus drift curves of a representative number of test specimens are compared to the corresponding analytical curves (ii) For cyclic loading, the... 

Next we examined the expected error when mixing the material models inappropriately. Eigure 6 shows the non-cyclic material model and the cyclic material model in comparison to the first cycle data. As expected, the first cycle material model provides a better prediction of the response. This is especially noticeable at higher displacements where the first cycle FEA prediction is much closer to the experimental data. We then looked at the two material models versus the 5 cycle experiment, Eigure 7, and we see that the cycled material model provides a superior prediction of the force/deflection curve. The cycled FEA, MR 15c, captures the cyclic softened response of the fifth cycle. One caveat is at maximum deflection, comparing the fifth cycle experimental data versus the FEA will show a divergence due to the experiment approaching the maximum strain previously seen. 

Figure 2 Prediction of the mechanical performance of a polymer product. Left Compression testing, maximum in ioad found at different rates. Inset experimental and numerical force versus displacement curves. Right Creep experiments, time to faiiure at different ioads. Symbois indicate experiments and lines indicate full predictions, including the influence of the different processing conditions used during the maidng of the product ...

Here, max and jrm n denote, respectively, the maximum and the minimum values of the muscular activation, a determines the slope of the feedback curve, S is the displacement of the curve along the flow axis, and Fneno is a normalization value for the Henle flow. The relation between the glomerular filtration and the flow into the loop of Henle can be obtained from open-loop experiments in which a paraffin block is inserted into the proximal tubule and the rate of glomerular filtration (or, alternatively, the so-called tubular stop pressure at which the filtration ceases) is measured as a function of an externally forced rate of flow of artificial tubular fluid into the loop of Henle. Translation of the experimental results into a relation between muscular activation and Henle flow is performed by means of the model, i.e., the relation is adjusted such that it can reproduce the experimentally observed steady state relation. We have previously discussed the significance of the feedback gain a in controlling the dynamics of the system, a is one of the parameters that differ between hypertensive and normotensive rats, and a will also be one of the control parameters in our analysis of the simulation results. 

The crystal lattice vibration and the force coefficients are the subject of Chapter 12. We describe the experimental dispersion curves and conclusions that follow from their examination. The interplanar force constants are introduced. Group velocity of lattice waves is computed and discussed. It allows one to make conclusions about the interatomic bonding strength. Energy of atomic displacements during lattice vibration (that is propagation of phonons) is related to electron structure of metals. 

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