Editing Poisson's ratio (section)

=== Anisotropic ===
For anisotropic materials, the Poisson ratio depends on the direction of extension and transverse deformation
:<math> \begin{align}
\nu (\mathbf{n}, \mathbf{m}) &= - E\left(\mathbf n\right) s_{ij \alpha \beta} n_i n_j m_\alpha m_\beta \\[4px]
E^{-1} (\mathbf{n}) &= s_{ij\alpha \beta } n_i n_j n_\alpha n_\beta 
\end{align}</math>

Here {{mvar|ν}} is Poisson's ratio, {{mvar|E}} is [[Young's modulus]], {{math|'''n'''}} is a unit vector directed along the direction of extension, {{math|'''m'''}} is a unit vector directed perpendicular to the direction of extension. Poisson's ratio has a different number of special directions depending on the type of anisotropy.<ref>{{Cite journal |last1=Epishin|first1=A. I. |last2=Lisovenko|first2=D. S. |date=2016 |title=Extreme values of Poisson's ratio of cubic crystals |journal=Technical Physics |language=en |volume=61 |issue=10 |pages=1516–1524 |doi=10.1016/j.mechmat.2019.03.017 |bibcode=2016JTePh..61.1516E |s2cid=140493258}}</ref><ref>{{Cite journal | last1=Gorodtsov|first1=V.A. | last2=Lisovenko|first2=D.S. | date=2019 | title=Extreme values of Young's modulus and Poisson's ratio of hexagonal crystals | journal=Mechanics of Materials |language=en |volume=134 |pages=1–8 |doi=10.1016/j.mechmat.2019.03.017 |bibcode=2019MechM.134....1G | s2cid=140493258}}</ref>