Poisson ratio defined

Here v represents the Poisson ratio, defined as the ratio between the linear contraction and the elongation in the axis of stretching. In the case of constant volume (an incompressible body like rubber), i> = 0.5 and therefore E = 3G for rigid materials p < 0.3. There is also a direct test for tear strength, mainly in the case of thin films, similar to those used in the paper industry. 

The ratio between these relative deformations is Ifn and can be used to define the deformation profile or length scale. Due to the presence of a softer back pad, more deformation is expected for the stacked pad but the shape, which is the main concern, will be approximately similar [45,46], The deformation is relatively small compared to the region of apphcation of the force. Using approximate material properties for the ICIOOO pad (Young s modulus of 2.9 x 10 Pa [41] and approximate Poisson ratio of 1/3) with force applied in a circular region of radius 2 mm, and a local pressure of 7 psi, the maximum deflection is about 6 fira. This deformation is referenced to the origin as illustrated in Fig. 13. It is also important to note that the transition shape is very gradual and this sets the polish limit for the down areas. 

Some properties are directly connected with mass and packing density (or its reciprocal specific volume), thermal expansibility and isothermal compressibility. Especially the mechanical properties, such as moduli, Poisson ratio, etc., depend on mass and packing. In this chapter we shall discuss the densimetric and volumetric properties of polymers, especially density and its variations as a function of temperature and pressure. Density is defined as a ratio ... 

The simplest mechanical properties are those of homogeneous isotropic and purely elastic materials their mechanical response can be defined by only two constants, e.g. the Young modulus E and the Poisson ratio v. For anisotropic, oriented-amorphous, crystalline and oriented-crystalline materials more constants are required to describe the mechanical behaviour. 

As just described, the deformed shape of the rubber sphere surrounded by an annulus of epoxy must be a perfect ellipsoid because the overall material is isotropic. As shown by equations 1 and 2, the deformed shape BC is defined from the Poisson ratio, and Youngs modulus can be calculated from summing the reactions. However, for the toughened material, the value of the Poisson ratio is not known only a relationship between E and v is known, as defined by K. Thus, the analysis of unidirectional loading for the spherical cell must be carried out using an iterative procedure. The method has been described in detail elsewhere (15). The results of the iteration can be verified by checking the reduction of the x reactions-to-earth to zero this verification was used for all the results presented here. 

A cylindrical fiber is subjected to elongational flow along the fiber axis such that the z-component of the velocity vector is = Az, where A is a positive constant that defines the rate of elongational flow. The fiber is isotropic with a Poisson ratio of 0.5, which means that there is no volume change during extensional flow. Newton s law of viscosity is valid to describe this phenomenon. 

For an isotropic body, there are only two stress components that are independent of the other. This means that while different loadings and strains can be imposed, the material constants relating stress and strain are not all unique. There are six common elastic constants (Table 6.1), including Poisson s ratio, defined as the ratio of the lateral strain accompanying a longitudinal strain, V = -eiilsn- Since only two are unique for an isotropic body, each elastic constant can be expressed as a function of any other pair these expressions are tabulated in Table 6.1 in terms of Poisson s ratio (Mott and Roland, 2009). 

The Poisson ratio can be used to characterize the mechanical property of a solid. It is defined as the negative quotient of the strain in the transverse direction to the strain applied in the longitudinal direction. For a uniaxial loading along the c-axis ... 

Hence, to define the elastic properties of the fiber, five independent components of elastic modulus are required—Axial Young s modulus En or ii ) Shear modulus (Gn or G ) Transverse Young s modulus (ii22 or Transverse Shear modulus (G22 or G ) and the Axial Poisson ratio (vi2 or v ). 

The elastic modulus E is only one of four elastic constants or modulae (8). Another one is the Poisson ratio i defined as... 

The shear modulus is suitable as a material property for FEM (Fig. 38). For Sikaflex adhesives, a Poisson ratio of 0.49 is suitable. The Poisson s ratio is defined in the Glossary in more detail. This value is needed in the Hooke s law ... 

The characteristic time defined in (9.21) establishes a time scale for surface evolution of the kind discussed in the preceding section. Its definition depends on a number of parameter values that are not measurable and, therefore, are not known with any certainty. To get some idea of its magnitude, estimate the value of the characteristic time for the particular case of a Si surface with a mismatch strain of Cin = 0.008 at a temperature of T = 600 °C. Base the estimate on the unit cell dimension of a = 0.5431 nm for the diamond cubic crystal structure, and on the following values of macroscopic material parameters an elastic modulus of E = 130 GPa, a Poisson ratio of = 0.25, a mass density oi p = 2328kg/m, and the surface energy of 70 = 2J/m. Assume that 10% of the surface atoms are involved in the mass transport process at any instant so that = 0.1. 

For a polymer film possessing orthorhombic symmetry, there are three lateral compliances 5i2, and S2i, which relate to the six Poisson s ratios defined in Section 8.2.2. 

Poisson s Ratio - This ratio is defined as the ratio of the change in the width per unit width of a material to the change in its length per unit length, as a result of strain in the length direction. At 23°C Poisson ratio of polytetrafluoroethylene has a value of 0.46. 

Another often useful material parameter is Poissons ratio, vp, which is defined as the ratio between the perpendicular (transverse) deformation (ALj in Figure 1.12) and the longitudinal deformation (AL) vp = -ALx/AL. In the general, viscoelastic case, similar considerations as in the case of shear flow hold for the temporal response of polymeric fluids at molecular scale, and the resulting macroscopic response. 

Poisson ratio When materials are subjected to a tensile strength, they stretch and become thinner in cross section. The Poisson ratio is defined as ... 

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