Poisson’s number

E is Young s modulus, G the shear modulus and m Poisson s number. The ratio of the rates in an isotropic medium is ... 

Table 1 The material constants of the SiC particle and the Si3N4 matrix [19]-[21] the Young s modulus, E the Poisson s number, p, the thermal expansion coefficient, a the yield stress in tension and compression, <3yt and o c, respectively the fracture toughness, Kic the SiC particle radius and volume fraction, R and v, respectively.

Table 1. Material mechanical properties (Oy - yield strength, E - elastic modulus, G - shear modulus, V - Poisson s number).

Table 1 Elastic Engineering Constants K, G, and E (in GPa) and Poisson s Number v, as Calculated from the Cited (7) Experimental Cy (in GPa) ...

The first constant is the inverse of the elastic modulus while the second is the negative ratio of Poisson s number and the elastic modulus. 

The fact that homogeneous samples shrink in the y- and z-direction if elongated in x-direction leads to a Poisson s number being greater than 0. (It must be also not greater than 1/2 owing to thermod5mamic criteria [91].)... 

Poisson s ratio at 125—375 K isotopes mass number natural abundance, %... 

In addition to chemical analysis a number of physical and mechanical properties are employed to determine cemented carbide quaUty. Standard test methods employed by the iadustry for abrasive wear resistance, apparent grain size, apparent porosity, coercive force, compressive strength, density, fracture toughness, hardness, linear thermal expansion, magnetic permeabiUty, microstmcture, Poisson s ratio, transverse mpture strength, and Young s modulus are set forth by ASTM/ANSI and the ISO. 

The designer must be aware that as the degree of anisotropy increases, the number of constants or moduli required to describe the material increases with isotropic construction one could use the usual independent constants to describe the mechanical response of materials, namely, Young s modulus and Poisson s ratio (Chapter 2). With no prior experience or available data for a particular product design, uncertainty of material properties along with questionable applicability of the simple analysis techniques generally used require end use testing of molded products before final approval of its performance is determined. 

When solving difference boundary-value problems for Poisson s equation in rectangular, angular, cylindrical and spherical systems of coordinates direct economical methods are widely used that are known to us as the decomposition method and the method of separation of variables. The calculations in both methods for two-dimensional problems require Q arithmetic operations, Q — 0 N og. N), where N is the number of the grid nodes along one of the directions. 

This means that Poisson s equation defines the potential with an uncertainty of a harmonic function 14. Regardless of a distribution of masses outside the volume the potential C4 remains harmonic function inside V and, correspondingly, there are an infinite number of potentials U which satisfy Equation (1.70), and they can be represented as ... 

This first case vividly illustrates the importance of the boundary condition. Indeed, Poisson s equation or the system of field equations have an infinite number of solutions corresponding to different distributions of masses located outside the volume. Certainly, we can mentally picture unlimited variants of mass distribution and expect an infinite number of different fields within the volume V. In other words, Poisson s equation, or more precisely, the given density inside the volume V, allows us to find the potential due to these masses, while the boundary condition (1.83) is equivalent to knowledge of masses situated outside this volume. It is clear that if masses are absent in the volume V, the potential C7 is a harmonic function and it is uniquely defined by Dirichlet s condition. 

Anisotropic materials have different properties in different directions (1-7). 1-Aamples include fibers, wood, oriented amorphous polymers, injection-molded specimens, fiber-filled composites, single crystals, and crystalline polymers in which the crystalline phase is not randomly oriented. Thus anisotropic materials are really much more common than isotropic ones. But if the anisotropy is small, it is often neglected with possible serious consequences. Anisoiropic materials have far more than two independent clastic moduli— generally, a minimum of five or six. The exact number of independent moduli depends on the symmetry in the system (1-7). Anisotropic materials will also have different contractions in different directions and hence a set of Poisson s ratios rather than one. 

To be specific we consider a planar electrode in contact with a solution of a z — z electrolyte (i.e., cations of charge number z and anions of charge number -z). We choose our coordinate system such that the electrode surface is situated in the plane at x = 0. The inner potential (x) obeys Poisson s equation ... 

Assuming that a number of NMR data sets (e.g., 2-D or 3-D maps of displacement vectors resulting from an external periodic excitation) from an object are acquired, the remaining difficulty is their reconstruction into viscoelastic parameters. As written in Section 2 the basic physical equation is a partial differential equation (PDE, Eq. (3)) relating the displacement vector to the density, the attenuation, Young s modulus and Poisson s ratio of the medium. The reconstruction problem is indeed two-fold ... 

Number of free valence electrons per atom Poisson s ratio... 

Values for V, and f/, for a number of metal oxide glass components are listed in Table 5.6. In a similar manner, the compressive modulus, K, and Poisson s ratio, v, can be determined using these parameters ... 

The analysis has shown that PAI may only be negative, and PAB ( both positive and negative. Therefore, the thermal effect accompanying a reversible stretching of the model depends on the ratio between p and PA,n and may be a function of strain even at small strains. Besides, Poisson s ratio for such a heterogeneous model may exeed 0.5, Direct measurements of Poisson s ratio for a number of various oriented crystalline polymers are consistent with this suggestion (see Table 5). 

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