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The value of Poisson's ratio is the negative of the ratio of transverse strain to axial strain. For small values of these changes, ν is the amount of transversal elongation divided by the amount of axial compression. Most materials have Poisson's ratio values ranging between 0.0 and 0.5.
Auxetic metamaterials are a type of metamaterial with a negative Poisson's ratio, so that axial elongation causes transversal elongation (in contrast to an ordinary material, where stretching in one direction causes compression in the other direction). Auxetics can be single molecules, crystals, or a particular structure of macroscopic matter ...
Some materials, known as auxetics, possess a negative Poisson's ratio because of their unique molecular structure. Because of this property, they experience a positive lateral strain alongside a positive longitudinal strain, and vice versa.
But the Poisson's ratio is neither constant nor does it have any fixed relationship with other moduli beyond the small strain regime. That can be verified by exploring any of a number of hyperelastic material models. My point is that using the term "Poisson's ratio" when we mean a more general "Poisson's effect" confuses rather than clarifies.
Materials with negative Poisson's ratio expand laterally when stretched, in contrast with ordinary materials. In comparing a material's resistance to distort under mechanical load rather than a change in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically.
Although the shear modulus, μ, must be positive, the Lamé's first parameter, λ, can be negative, in principle; however, for most materials it is also positive. The parameters are named after Gabriel Lamé. They have the same dimension as stress and are usually given in SI unit of stress [Pa].
Which is why the woman took the time to make a video about the Doxie. Someone else needs to get to know this good boy. It was the woman's mission to find the Dachshund a home before the holidays.
The traditional negative binomial regression model is based on the Poisson-gamma mixture distribution. This model is popular because it models the Poisson heterogeneity with a gamma distribution. Poisson regression models are generalized linear models with the logarithm as the (canonical) link function , and the Poisson distribution function as ...