Question

How many independent material constants in solids are required to define isotropic materials?

• A. 2
• B. 3
• C. 9
• D. 21

Hint:

1. For isotropic materials, use any two constants from \( E, \nu, G, K \), with relationships to derive others.
2. For anisotropic materials, more constants (up to 21) are required to define mechanical behavior.
3. Remember that isotropy simplifies material behavior analysis significantly.

Answer 1

The Correct Option is A

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 \( \mathbf{(A)} \).