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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Poisson’s ratio ： ウィキペディア英語版 Poisson's ratio Poisson's ratio, named after Siméon Poisson, also known as the coefficient of expansion on the transverse axial, is the negative ratio of transverse to axial strain. When a material is compressed in one direction, it usually tends to expand in the other two directions perpendicular to the direction of compression. This phenomenon is called the Poisson effect. Poisson's ratio $\backslash nu$ (nu) is a measure of this effect. The Poisson ratio is the fraction (or percent) of expansion divided by the fraction (or percent) of compression, for small values of these changes. Conversely, if the material is stretched rather than compressed, it usually tends to contract in the directions transverse to the direction of stretching. This is a common observation when a rubber band is stretched, when it becomes noticeably thinner. Again, the Poisson ratio will be the ratio of relative contraction to relative expansion, and will have the same value as above. In certain rare cases, a material will actually shrink in the transverse direction when compressed (or expand when stretched) which will yield a negative value of the Poisson ratio. The Poisson's ratio of a stable, isotropic, linear elastic material cannot be less than −1.0 nor greater than 0.5 due to the requirement that Young's modulus, the shear modulus and bulk modulus have positive values.〔H. GERCEK; “''Poisson's ratio values for rocks''”; International Journal of Rock Mechanics and Mining Sciences; Elsevier; January 2007; 44 (1): pp. 1–13〕 Most materials have Poisson's ratio values ranging between 0.0 and 0.5. A perfectly incompressible material deformed elastically at small strains would have a Poisson's ratio of exactly 0.5. Most steels and rigid polymers when used within their design limits (before yield) exhibit values of about 0.3, increasing to 0.5 for post-yield deformation which occurs largely at constant volume.〔Park, RJT. ''Seismic Performance of Steel-Encased Concrete Piles''〕 Rubber has a Poisson ratio of nearly 0.5. Cork's Poisson ratio is close to 0: showing very little lateral expansion when compressed. Some materials, mostly polymer foams, and materials with special geometries such as zigzag-based materials can have a negative Poisson's ratio; if these auxetic materials are stretched in one direction, they become thicker in perpendicular direction. Some anisotropic materials, such as zigzag-based folded sheet materials,〔 have one or more Poisson's ratios above 0.5 in some directions. Assuming that the material is stretched or compressed along the axial direction (the ''x'' axis in the below diagram): :$\backslash nu\; =\; -\backslash frac\}\; =\; -\backslash frac\}=\; -\backslash frac\}$ where :$\backslash nu$ is the resulting Poisson's ratio, :$\backslash varepsilon\_\backslash mathrm$ is transverse strain (negative for axial tension (stretching), positive for axial compression) :$\backslash varepsilon\_\backslash mathrm$ is axial strain (positive for axial tension, negative for axial compression). == Length change == For a cube stretched in the ''x''-direction (see figure 1) with a length increase of $\backslash Delta\; L$ in the ''x'' direction, and a length decrease of $\backslash Delta\; L\text{'}$ in the ''y'' and ''z'' directions, the infinitesimal diagonal strains are given by :$$ d\varepsilon_x=\frac\qquad d\varepsilon_y=\frac\qquad d\varepsilon_z=\frac. Integrating these expressions and using the definition of Poisson's ratio gives :$$ -\nu \int\limits_L^\frac=\int\limits_L^\frac=\int\limits_L^\frac. Solving and exponentiating, the relationship between $\backslash Delta\; L$ and $\backslash Delta\; L\text{'}$ is then :$$ \left(1+\frac\right)^ = 1-\frac. For very small values of $\backslash Delta\; L$ and $\backslash Delta\; L\text{'}$, the first-order approximation yields: :$$ \nu \approx \frac. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Poisson's ratio」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.