I know the range of poisson's ratio is -1 to 0.5 but how do you arrive at this expression? I am a 11th grade student and I am not too familiar with advanced physics
Answer
The answer is a bit lengthy, but can be arrived at using arguments about elastic strain energy. Here is a very detailed explanation:
Limits of Poisson's ratio in isotropic solid
This was written at a graduate mechanical engineering level, so I'll simplify it here.
Imagine that there exists a function $\psi$ that describes how much energy is contained in a solid per unit volume. This quantity is a function of material properties and deformation. For a linear elastic, isotropic solid, the material properties are Young's modulus (E), and the Poisson ratio ($\nu$).
One of the assumptions of the theory of elasticity is that the elastic energy $\psi$ is a function that is strictly increasing for all conceivable deformations. The details of this assumption are in my other answer (the link), but it turns out that $\nu$ can only be in the interval
$$ -1 < \nu < \frac{1}{2} $$
I hope this clears up your question at an appropriate level. Let me know in the comments if not!
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