Discussion
If the Poisson's ratio for a material is 0.5, then the elastic modulus for the material is:
Answer: A
The elastic modulus is three times its shear modulus.
Young's modulus and the shear modulus are linked by Poisson's ratio \(\mu\):
\[ \begin{aligned} E &= 2G(1 + \mu) \\ &= 2G(1 + 0.5) = 3G \end{aligned} \]
A Poisson's ratio of 0.5 describes an incompressible material, such as rubber, for which this result is used. Four times would need \(\mu = 1\), which is impossible for a stable isotropic material, while 'equal to' and 'half of' would need \(\mu\) of \(-0.5\) and \(-0.75\).
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