Category : JEE Main & Advanced
Moduli of elasticity are three, viz. Y, K and \[\eta \] while elastic constants are four, viz, Y, K, \[\eta \] and \[\sigma \]. Poisson's ratio s is not modulus of elasticity as it is the ratio of two strains and not of stress to strain. Elastic constants are found to depend on each other through the relations :
\[Y=3K(1-2\sigma )\] ...(i)
\[Y=2\eta (1+\sigma )\] ...(ii)
Eliminating s or Y between these, we get
\[Y=\frac{9K\eta }{3K+\eta }\] ...(iii)
\[\sigma =\frac{3K-2\eta }{6K+2\eta }\] ...(iv)
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