Question

If \( G \) denotes the shear modulus of an isotropic material, then the maximum possible value of Young's modulus of the material is

• A. \( G \)
• B. \( 2G \)
• C. \( 3G \)
• D. \( 4G \)

Hint:

Use the relation \( E = 2G(1+\nu) \); the maximum \( E \) occurs at the maximum allowable Poisson's ratio \( \nu = 0.5 \).

Answer 1

The Correct Option is C

For isotropic materials, Young's modulus \( E \), shear modulus \( G \), and Poisson's ratio \( \nu \) are related by \[ E = 2G(1 + \nu). \] The Poisson's ratio for isotropic materials lies within \[ -1 < \nu < \tfrac{1}{2}. \] Thus, the maximum value occurs at \( \nu = \tfrac{1}{2} \), giving \[ E_{\max} = 2G \left( 1 + \tfrac{1}{2} \right) = 3G. \] So the largest physically possible Young's modulus for an isotropic material is \( 3G \).
Final Answer: \( 3G \)