Static elasticity

Resistance-Deflection Function. The resistance-deflection function establishes the dynamic resistance of the trial cross-section. Figure 4a shows a typical design resistance-deflection function with elastic stiffness, Kg (psi/in), elastic deflection limit, Xg (in) and ultimate resistance, r.. (psi). The stiffness is determined from a static elastic analysis using the average moment of inertia of a cracked and uncracked cross-section. (For design... 

Pressure-area (jt-A) isotherms were obtained at various Tsps with a microprocessor-controlled film balance system. The static elasticity, Ks of the monolayer on the water surface was evaluated from the jr-A isotherm by using the following equation 1-3],... 

Indices are dimensionless parameters derived from various mechanical and physical properties of the tablet blend and resulting compacts. Mechanical properties typically measured include indentation hardness (kinetic and static), elastic modulus, and tensile strength (10,11). Physical properties include particle size, shape, and size distribution, density (true, bulk, and tapped), flow properties and cohesive properties. 

Fig. 11 77 and es vs. A isotherms for PVAc on water at 230 C. Surface pressure 77 (represented by the circles) and the static elasticity es (represented by the solid curve) are plotted as a function of area per monomer. The open circles atlarge A correspond to good solvent conditions. The filled circles correspond to the region of increasing es as well as deviation from a power law scaling. The open circles at small A correspond to a collapsing film... 

Continuing to use PVAc as the canonical example of a stable and easily reproducible polymer monolayer, we show how the two quantities, the static elasticity es from 77-A the isotherm, and the corresponding ej deduced from the SLS experiment, compare and contrast with each other for the time being, we defer to later the SLS results. This is shown in Fig. 12. Agreement between the two is remarkable up to respective maximum points. The observed deviation at higher 77 is not expected since the monolayer state is no longer maintained, hence the static elastic responses in macroscopic scales are not likely to be the same as the dynamic response to spontaneous capillary waves. 

Having shown how the static lateral modulus ss, also called static elasticity, is determined from IJ-A isotherm via Eq. 8, we return to the three classes of homopolymers. Plots of es against /7 are shown in Fig. 13, where the re-... 

Fig. 27 77 - F isotherms (a) and e - F for sample I (PEO-PPO-PEO) on the air/water interface at various temperatures 9 °C ( ), 23 °C, ( ) and 30 °C (A). F indicates the surface mass density where the static elasticity at 9 °C reaches the maximum, not the onset point of semi-dilute solution...

Figure 31 shows (a) and /< (b) - / plots for sample II, 10R5 (PPO-PEO-PPO). Dynamic dilational elasticities s at different temperatures reach their asymptotes at the same concentration ( 0.5 mgm 2) but a bit higher than r (0.4 mg nr2). Corresponding viscosities /< at three different temperatures reach the minima at the same value of r as the static elasticities of this poly-... 

On the basis of our experimental results presented so far, the overall viscoelastic behavior of these triblock copolymers shows an elasticity-dominance over the viscosity. After reaching the critical mass density, where the static elasticity es reaches the maximum, these triblock copolymers collapse into the subphase and form hydrated brushes and these anchored brushes may be responsible for the result that the surface viscosities drop to around the 0 value at r. A distinctive difference between two types of polymers, sample I (PEO-PPO-PEO) and sample II (PPO-PEO-PPO), is the temperature dependence of r where both static elasticity and dilational viscosity show kinds of transitions. V of sample I increases with increasing temperature while that of sample II does not change with temperature. 

The grafted layer also affects two other features of the rheology. First, thicker polymer layers enhance the elasticity due to the longer range of the repulsion relative to the hard core size. Thus, samples formulated at 4>cff mo possess easily measurable static elastic moduli. Second, the softer repulsion apparently suppresses the shear thickening observed at high volume fractions for the harder particles, in accordance with earlier measurements by Willey and Macosko (1978). 

Qualitatively, the Middle Atlantic Bight samples were very similar to those collected in the California Bight. The predominant components were the same in both locales, suggesting that a limited number of compound classes are dominant in microlayer films, but present in varying proportions. The specific mixtures of surfactants in the microlayers sampled in this study strongly influenced air-sea interfacial quasi-static elasticity. Pre-... 

Abstract. Variations in the chemical composition of surfactants from natural sea slicks are compared to variations in surface elasticity using mass spectrometry, Langmuir film balance measurements, and multivariate statistical techniques. It is shown that the information on chemical class and molecular structure contained in the mass spectra is strongly correlated with measured static elasticity and can be used to estimate film elasticity at a given surface pressure. 

The Chemometricks analysis developed discriminant functions that distinguished each sample or sample class from every other based on the principal mass components of the spectra. Applied to individual spectra, the discriminant functions yielded a function score that reflected the abundance of those chemical components in the sample mixture that distinguished the sample or class from the others. Experimentally measured static elasticities for the samples were then compared with the discriminant scores to determine the degree of correlation between the spectral patterns and surface elasticity. 

Corresponding film pressure values P surfactant concentration P calculated from the wavelength measurements are shown in Figure 3, arrow bars are shown in the last graphic. In Figure 3 the static elasticity values, estimated from the pressure-concentration curves as H / JdP/dP) are also presented (the scale for the values of elasticity and film pressure is the same). 

Fig. 3. Film pressure-concentration curves, retrieved from wavelength measurements for films of oleyl alcohol (a), oleic acid (b) and Emkarox (c). o - static elasticity values...

In spite of these quantitative differences, qualitatively the behaviour of the static elasticity curves are similar in Figures 3 and 4 the elasticity achieves a maximum at small concentrations of the order of a saturated monolayer concentration and then decreases very quickly tending to small values for saturated films. 

The estimated dynamic elasticity of the polymer film also differs from the static elasticity. The dynamic elasticity increases with concentration, achieving a maximum at intermediate concentrations (between the two damping coefficient maxima), and then decreases monotoniously to small values at large concentrations. 

Trend in chemical shifts, relaxation times, and quadrupolar coupling reported by Yamagata Hackeloer and Kanert use gradient-elastic constants determined through monitoring change in spectrum with static elastic stress... 

Marsh and Casabella induced elastic strain upon single crystals of NaCl and NaBr by plying static pressure (up to 6.9 MPa) and noted, as expected, that the C1 and Br NMR lineshapes broadened and became less intense. The authors determined that the purely ionic model of vK was inadequate to describe the changing field gradients at the chlorine and bromine nuclei with respect to changing pressure. It was concluded that ion orbital overlap between nearest and NNN atoms was a satisfactory model to rationalize their observations and that pure covalent effects did not need to be included. The effects of static elastic strain on chlorine SSNMR spectra were observed to determine the gradient-elastic tensors for LiCl and RbCl by Flackeloer and Kanert. ... 

Bending Strain Static elastic modulus (Young s Modulus, i.e., the slope of the stress-strain curve in the elastic region) Crystalline morphological transitions... 

The simplest approach to analyzing viscous flow is to continue with the previous assumptions. The primary assumption is that the motion is slow, with negligible inertial forces. This allows terms involving acceleration, which lead to non-linearities in the equations, to be neglected and thereby preserves the analogy with static elasticity. 

M. Helvatjoglu-Antoniades, Y. Papadogiannis, R.S. Lakes, P. Dionysopoulos, D. Papadogiannis, Dynamic and static elastic moduh of packahle and flowable composite resins and their development after initial photo curing. Dent. Mater. 22 (2006) 450-459. 

Compressive strength ratio -Ratio of static elastic modulus Ratio of dynamic elastic modulus... 

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