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Poisson's ratio of a material defines the ratio of transverse strain (x direction) to the axial strain (y direction)In materials science and solid mechanics, Poisson's ratio (symbol: ν ()) is a measure of the Poisson effect, the deformation (expansion or contraction) of a material in directions perpendicular to the specific direction of loading.
k! = k(k–1) ··· (3)(2)(1) is the factorial. The positive real number λ is equal to the expected value of X and also to its variance. [13] = = (). The Poisson distribution can be applied to systems with a large number of possible events, each of which is rare. The number of such events that occur during a fixed time interval is ...
where K is the stress intensity factor (with units of stress × length 1/2) and is a dimensionless quantity that varies with the load and geometry. Theoretically, as r goes to 0, the stress σ i j {\displaystyle \sigma _{ij}} goes to ∞ {\displaystyle \infty } resulting in a stress singularity. [ 5 ]
2 Poisson's ratio. 3 Bulk modulus. 4 Shear modulus. 5 References. 6 See also. Toggle the table of contents. Elastic properties of the elements (data page) 1 language.
the Poisson's ratio ν describes the response in the directions orthogonal to this uniaxial stress (the wire getting thinner and the column thicker), the bulk modulus K describes the material's response to (uniform) hydrostatic pressure (like the pressure at the bottom of the ocean or a deep swimming pool),
The two parameters together constitute a parameterization of the elastic moduli for homogeneous isotropic media, popular in mathematical literature, and are thus related to the other elastic moduli; for instance, the bulk modulus can be expressed as K = λ + 2 / 3 μ.
The earliest published example of a material with negative Poisson's constant is due to A. G. Kolpakov in 1985, "Determination of the average characteristics of elastic frameworks"; the next synthetic auxetic material was described in Science in 1987, entitled "Foam structures with a Negative Poisson's Ratio" [1] by R.S. Lakes from the ...
The Poisson's ratio is a measure in which a material tends to expand in directions perpendicular to the direction of compression. After measuring the Young's modulus and the shear modulus, dedicated software determines the Poisson's ratio using Hooke's law which can only be applied to isotropic materials according to the different standards.