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Most materials have Poisson's ratio values ranging between 0.0 and 0.5. For soft materials, [1] such as rubber, where the bulk modulus is much higher than the shear modulus, Poisson's ratio is near 0.5. For open-cell polymer foams, Poisson's ratio is near zero, since the cells tend to collapse in compression.
Material properties are most often characterized by a set of numerical parameters called moduli. The elastic properties can be well-characterized by the Young's modulus, Poisson's ratio, Bulk modulus, and Shear modulus or they may be described by the Lamé parameters.
The Poisson distribution is a special case of the discrete compound Poisson distribution (or stuttering Poisson distribution) with only a parameter. [33][34] The discrete compound Poisson distribution can be deduced from the limiting distribution of univariate multinomial distribution.
In index notation: The inverse relationship is [12] Therefore, the compliance tensor in the relation ε = s : σ is In terms of Young's modulus and Poisson's ratio, Hooke's law for isotropic materials can then be expressed as This is the form in which the strain is expressed in terms of the stress tensor in engineering.
Gauge factor (GF) or strain factor of a strain gauge is the ratio of relative change in electrical resistance R, to the mechanical strain ε. The gauge factor is defined as: [ 1 ] where. ε = strain = Δ L. = absolute change in length. = original length. ν = Poisson's ratio.
Poisson summation formula. In mathematics, the Poisson summation formula is an equation that relates the Fourier series coefficients of the periodic summation of a function to values of the function's continuous Fourier transform. Consequently, the periodic summation of a function is completely defined by discrete samples of the original ...
Poisson limit theorem. In probability theory, the law of rare events or Poisson limit theorem states that the Poisson distribution may be used as an approximation to the binomial distribution, under certain conditions. [1] The theorem was named after Siméon Denis Poisson (1781–1840). A generalization of this theorem is Le Cam's theorem.
In the low-frequency limit for the extensional mode, the z- and x-components of the surface displacement are in quadrature and the ratio of their amplitudes is given by: where is Poisson's ratio.