Lateral strain ratio

The modulus term in this equation can be obtained in the same way as in the previous example. However, the difference in this case is the term V. For elastic materials this is called Poissons Ratio and is the ratio of the transverse strain to the axial strain (See Appendix C). For any particular metal this is a constant, generally in the range 0.28 to 0.35. For plastics V is not a constant. It is dependent on time, temperature, stress, etc and so it is often given the alternative names of Creep Contraction Ratio or Lateral Strain Ratio. There is very little published information on the creep contraction ratio for plastics but generally it varies from about 0.33 for hard plastics (such as acrylic) to almost 0.5 for elastomers. Some typical values are given in Table 2.1 but do remember that these may change in specific loading situations. 

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. 

Poison s ratio It is the proportion of lateral strain to longitudinal strain under conditions of uniform longitudinal stress within the proportional or elastic limit. When the material s deformation is within the elastic range it results in a lateral to longitudinal strain that will always be constant. In mathematical terms, Poisson s ratio is the diameter of the test specimen before and after elongation divided by the length of the specimen before and after elongation. Poisson s ratio will have more than one value if the material is not isotropic... 

E. Konofagou and J. Ophir, A new elastographic method for estimation and imaging of lateral displacements, lateral strains, corrected axial strains and Poisson s ratios in tissues, Ultrasound Med. Biol., 1998, 24, 1183-1199. 

Poisson s ratio-ratio of lateral strain to axial strain in an axial loaded specimen. It is a constant that relates the modulus of rigidity to Young s modulus. 

Figure 2b Variation of Poisson s ratio as a function of lateral strain...

As indicated in Figure 3.1, an elongation (or compression) in one direction, due to an axial force, produces a contraction (or expansion) in the lateral direction, i.e., at right angles to the direction of the force. The ratio of the lateral strain to the longitudinal strain is called Poisson s ratio v. It is an important elastic constant. For instance, a tensile stress, (t which produces a tensile strain, in the x-direction will also produce a contractive strain, Sy, in the y-direction, the two being related by... 

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). 

During the above experiments measurements of the lateral strain in the sheet thickness direction were also made. The ratio of this strain to the tensile strain, designated vu, (t, ff), has been derived for t = 100 s and various values of 0. This data for tensile strains in the range 1-6% is presented. 

Strain to the longitudinal strain in a Stretched rod. If the original diameter of the rod is d and the contraction of the diameter under stress is Ad, the lateral strain Ad/d= ss if the original length is I and the extension under stress Al, the longitudinal strain is All I = 1. Poisson s ratio is then s /si. For steels the value is between 0.28 and 0.30 and for aluminium alloys It Is about 0.33. It was first introduced by Simeon Poisson (1781-1840). 

Poisson s ratio Ratio of lateral strain to axial strain in axially loaded specimen. 

Where a is the longitudinal stress, e is corresponding strain, and E is called Young s modulus (or the modulus of elasticity). Similarly, in shear deformation, the modulus is called the shear modulus or the modulus of rigidity (G). When a hydrostatic force is applied, a third elastic modulus is used the modulus of compressibility or bulk modulus (K). It is defined as the ratio of hydrostatic pressure to volume strain. A deformation (elongation or compression) caused by an axial force is always associated with an opposite deformation (contraction or expansion) in the lateral direction. The ratio of the lateral strain to the longitudinal strain is the fourth elastic constant called Poisson s ratio (v). For a small deformation, elastic parameters can be correlated in the following way ... 

When a solid body is being stretched (or compressed) by a uniaxially applied force, it will undergo extension (or compression) in the direction in which the force is acting. This deformation will also be accompanied by a lateral one a contraction if the axial deformation is in extension, or an expansion if the axial force is in compression. For a body, that is homogeneous and isotropic, the ratio of lateral strain to the corresponding axial strain is a constant known as Poisson s ratio. 

The ratio between lateral strain to axial strain Sj/e, increases firstly, then decreases and finally keeps constant as plastic strain increases under confining pressure 1 MPa and 30 MPa. There is no decreasing section in the curve of rock specimen under intermediate confining pressures 15 MPa ... 

The effective axial Poisson s ratio is dehned as the negative ratio of lateral strain 2 when nnder axial strain 1 and cti 0 and all the other stresses are identically zero. 

A fourth elastic material constant is Poisson s ratio, v. In an axial loading of a metal sample the specimen is strained and becomes longer. At the same time a lateral strain occurs and the sample becomes a little thinner. Poisson s ratio is the ratio of the lateral strain to the uniaxial strain. Its value is typical for an element and is in general close to 1/3. 

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