The value of Poisson's ratio lies between

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Question

(A) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and Modulus of rigidity $(\eta)$ with Poisson's ratio $(\sigma)$ is given by:$Y

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$-1$ to $\frac{1}{2}$

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(A) The relationship between Young's modulus $(Y)$,Bulk modulus $(K)$,and Modulus of rigidity $(\eta)$ with Poisson's ratio $(\sigma)$ is given by:$Y = 3K(1 - 2\sigma)$$Y = 2\eta(1 + \sigma)$For a stable material,the moduli of elasticity must be positive $(Y, K, \eta > 0)$.From $Y = 3K(1 - 2\sigma) > 0$,we get $1 - 2\sigma > 0$,which implies $\sigma From $Y = 2\eta(1 + \sigma) > 0$,we get $1 + \sigma > 0$,which implies $\sigma > -1$.Therefore,the theoretical range for Poisson's ratio is $-1 < \sigma < \frac{1}{2}$.

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