How many independent material constants in solids are required to define isotropic materials?
Show Hint
2. For anisotropic materials, more constants (up to 21) are required to define mechanical behavior.
3. Remember that isotropy simplifies material behavior analysis significantly.
- 2
- 3
- 9
- 21
The Correct Option is A
Solution and Explanation
Step 1: Material properties for isotropic solids. Isotropic materials exhibit uniform properties in all directions. The behavior of such materials is defined using two independent material constants, commonly: - Young's modulus (\( E \)) - Poisson's ratio (\( \nu \)) Alternatively, other pairs of constants like shear modulus (\( G \)) and bulk modulus (\( K \)) can also be used, with relationships connecting them.
Step 2: Analyze the options.
Option (A): 2 — Correct. Isotropic materials require only two independent constants to describe their mechanical behavior. Option (B): 3 — Incorrect. Three constants are not necessary as two are sufficient for isotropic materials. Option (C): 9 — Incorrect. Nine constants are required for anisotropic materials, not isotropic ones. Option (D): 21 — Incorrect. 21 constants are for the most general anisotropic materials.
Conclusion: To define isotropic materials, \( \mathbf{2} \) independent material constants are required, corresponding to option \( \mathbf{(A)} \).
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