For a material that is inelastic and anisotropic, how many independent elastic constants are required to describe its stress-strain relationship under small deformations using Hooke’s law?
- A2
- B6
- C21
- DNoneCorrect
Solution
Concept
Applicability of Hookes law to inelastic materials
Formula
NONE
Step-by-step solution
1. Hooke's law defines a linear constitutive relation between stress and strain: σ = C × ε. 2. This formulation strictly requires the material to behave in an elastic manner within its proportional limit. 3. For an inelastic material, plastic flow and permanent strain develop, making linear elasticity inapplicable. 4. Consequently, no elastic constants (None) can describe the stress-strain behavior using Hooke's law. Answer: D
Explanation
Hooke's law defines a linear relationship between stress and strain strictly for elastic materials within their proportional limit. For an inelastic material, plastic or permanent deformations occur, and Hooke's law cannot describe the constitutive behavior. Therefore, zero (none) elastic constants are applicable.
Why the other options are wrong
A) 2 applies to linearly elastic isotropic materials. B) 6 is not the standard count for general elastic anisotropy. C) 21 applies strictly to an anisotropic material that is linearly ELASTIC.
Shortcut
Inelastic material = Hooke's law invalid = Zero (None) elastic constants applicable.
Common mistake
Selecting 21 by assuming the material is anisotropic elastic rather than noticing "inelastic".
Correct answer: D) None