For an isotropic, homogeneous and elastic material obeying Hooke's law, the number of independent elastic constants is:
Try it first: pick an option, then read the explanation.
Correct answer: D. None of these
Asked in SSC JE 29/01/2018 (Morning)
Detailed Explanation
There are four common elastic constants: E, G, K and μ. They are linked by relations such as E = 2G(1 + μ) and E = 3K(1 − 2μ).
Why “None of these” Is Correct
Because of these two relations, knowing any two constants fixes the other two. So an isotropic material has 2 independent elastic constants. Since 2 is not among the options, the answer is (d).
| Material | Independent elastic constants |
|---|---|
| Isotropic | 2 |
| Orthotropic (e.g. wood) | 9 |
| Anisotropic (general) | 21 |
Why the Other Options Are Wrong
- A. 3: 3 is not correct for isotropic materials.
- B. 1: One constant is not enough to describe both stiffness and Poisson's effect.
- C. 9: 9 is for orthotropic materials.
Key Point
Isotropic: 2 independent constants; orthotropic: 9; anisotropic: 21.
Key Concepts for Students
- Usually E and μ are chosen as the two.
- Wood and fibre composites are orthotropic.
- Crystals are generally anisotropic.
Practice more: this is question 24 in Stress and Strain MCQs – Part 2. Try the whole set and check every answer instantly.