Why Poisson’s Ratio Cannot be Greater than 0.5

Theoretically the Poisson ratio should be in between -1 and 0.5 because of the following requirement :

the modulus of elasticity (E ), modulus of rigidity (G), and bulk modulus must be positive

Now remember the following basic relations of physics :

G=E/(2(1+n))………1

K=E/(3(1-2n))……..2

where,
n – Poisson’s ratio

now from the equation1 it can be seen that the value of poisson ratio cannot be smaller than -1 in order to keep G positive.

Similarly from the equation2 it can be concluded that the value of the Poisson’s ratio (n) cannot be greater than 0.5 to keep the bulk modulus (K) positive.

Although, the theoretical range for the Poisson ratio is negative one to 0.5, but practically, the value of it lies between zero and 0.5 only.

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