Elastic negative

Pi = approximate true radius of the circle defined by all zero points of the diagram of the elastic negative radial moments produced by the loads, assuming an elastic fixity of the slab periphery. 

The absolute values of the negative radial moments decrease from the periphery to the centre of the cap. Obviously, the maximum absolute value of these moments corresponds to the cap periphery. For particular purposes it is first necessary to obtain the position of the zero point of the elastic negative radial moment. Subsequently, the fulfilment of the condition is obtained when radial steel reinforcement is placed along the length of the above-mentioned moment diagram so that... 

Wensink et al. [556] compared a variety of masking materials. The best results for powder blasting of structures with dimensions larger than 50 pm have been achieved using BF 400, which is an elastic negative photoresist foil. 

It is necessary to establish some conventions concerning signs before proceeding further. When the applied force is a tensile force and the distortion is one of stretching, F, dL, and dw are all defined to be positive quantities. Thus dw is positive when elastic work is done on the system. The work done by the sample when the elastomer snaps back to its original size is a negative quantity. 

Another commonly used elastic constant is the Poisson s ratio V, which relates the lateral contraction to longitudinal extension in uniaxial tension. Typical Poisson s ratios are also given in Table 1. Other less commonly used elastic moduH include the shear modulus G, which describes the amount of strain induced by a shear stress, and the bulk modulus K, which is a proportionaHty constant between hydrostatic pressure and the negative of the volume... 

In six-dimensional strain space, may be viewed as the inner produet of the normal to the elastic limit surface and the tangent to the strain history , see Fig. 5.1. Its value is negative, zero, or positive depending on whether i, points inward, along the tangent, or outward to the elastic limit surface. Four cases may be distinguished. 

For, suppose that this inequality is not true, and that becomes negative at t = t. The smoothness assumptions that have been made imply that the integrand must continue to be negative for at least a short finite-time interval Ar. Now a second cycle may be chosen which is identical with tj) over the time interval (tf, tf + At), but in which elastic unloading commences at time t f + At. Since is zero during elastic portions of the cycle, the integral of is negative for this second cycle, which contradicts (5.50). 

One final point. We earlier defined Poisson s ratio as the negative of the lateral shrinkage strain to the tensile strain. This quantity, Poisson s ratio, is also an elastic constant, so we have four elastic constants E, G, K and v. In a moment when we give data for the elastic constants we list data only for . For many materials it is useful to know that... 

Now, as the crack grows into the plate, it allows the material of the plate near the crack to relax, so that it becomes less highly stressed, and loses elastic energy. 8Lf is thus negative, so that is positive, as it must be since G,- is defined positive. We can... 

The rise times of the elastic wave may be quite narrow in elastic single crystals, but in polycrystalline solids the times can be significant due to heterogeneities in physical and chemical composition and residual stresses. In materials such as fused quartz, negative curvature of the stress-volume relation can lead to dispersive waves with slowly rising profiles. 

A limited number of minus-x orientation samples were impact loaded in the vicinity of the Hugoniot elastic limit at stresses from 5.9 to 6.7 GPa. The principal observation of these experiments was that positive currents were observed from negative polarity disks when a stress of 5.9 GPa was exceeded. Such an observation confirms that quartz responds as predicted by the model, and that the elastic limit is in the vicinity of 6 GPa. 

The preceding restrictions on engineering constants for orthotropic materials are used to examine experimental data to see if they are physically consistent within the framework of the mathematical elasticity model. For boron-epoxy composite materials, Dickerson and DiMartino [2-3] measured Poisson s ratios as high as 1.97 for the negative of the strain in the 2-direction over the strain in the 1-direction due to loading in the 1-direction (v 2)- The reported values of the Young s moduli for the two directions are E = 11.86 x 10 psi (81.77 GPa) and E2 = 1.33x10 psi (9.17 GPa). Thus,... 

When a bar is elongated axially, as in Figure 2-25, it will contract laterally. The negative ratio of the lateral strain to the axial strain is called Poisson s ratio v. For isotropic materials, materials that have the same elastic properties in all directions, Poisson s ratio has a value of about 0.3. 

The writer45 60 has criticized the elasticity theory model on the basis that this partial character renders the theory unverifiable by experiment, unless this model is correlated with another model that may be postulated to represent the negative portion of the AH, a correlation which has never been achieved. Another criticism has been the inconsistency of the model when it is applied to the case of solute atom smaller than the solvent atom, as opposed to... 

The negative sign indicates that all real fluids contract when the pressure increases. Since Bv/v is a mere number, the elasticity has the same dimensions as pressure. 

Velocity profiles are demonstrated from Figs. 6 and 7. Figure 6 shows the effects of the viscosity-to-elasticity ratio at negative and positive normal stress gradients. Figure 7 shows the effects of various normal stress gradients on velocity profiles at the value of = 0.6. No general conclusions can be drawn... 

B. Mosaic Stiffening and Temperature Evolution of the Boson Peak The Negative Griineisen Parameter An Elastic Casimir Effect ... 

VI. THE NEGATIVE GRUNEISEN PARAMETER AN ELASTIC CASIMIR EFFECT ... 

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