Question:
If \( G \) denotes the shear modulus of an isotropic material, then the maximum possible value of Young's modulus of the material is
If \( G \) denotes the shear modulus of an isotropic material, then the maximum possible value of Young's modulus of the material is
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Use the relation \( E = 2G(1+\nu) \); the maximum \( E \) occurs at the maximum allowable Poisson's ratio \( \nu = 0.5 \).
Updated On: Jan 13, 2026
- \( G \)
- \( 2G \)
- \( 3G \)
- \( 4G \)
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The Correct Option is C
Solution and Explanation
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: \( 3G \)
Final Answer: \( 3G \)
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