Why \(\nu=\frac{1}{4}\)

The definition of Poisson’s ratio as the ratio of lateral strain \(\epsilon_{22}\) to longitudinal strain \(\epsilon_{11}\) defines the elastic constant \[\nu=-\frac{\epsilon_{22}}{\epsilon_{11}}\] Generally we speak of Poisson’s ratio \(\nu\) as a clear concept. But from where it came? and why the admissible values is limited to a certain range? This is a very interesting story that I will attempt to tell here.

Elasticity theory