Poisson’s ratio — general bound For stable, common engineering materials, the numerical value of Poisson’s ratio ν is generally:
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AGreater than 1
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BLess than 1
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CExactly equal to 1
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DUndefined for solids
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ENegative for all metals
Answer
Correct Answer: Less than 1
Explanation
Introduction / Context:Poisson’s ratio ν characterizes lateral strain response to axial strain in linear elasticity. Realistic bounds aid quick checks of test data and models.
Given Data / Assumptions:
- Isotropic, linear-elastic solids with positive stiffness.
- No auxetic (negative ν) specialty materials considered.
Concept / Approach:For a stable isotropic elastic material, the elastic moduli relationships require −1 < ν < 0.5 for positive definiteness (positive bulk and shear moduli). Most metals lie around 0.25 to 0.35, concretes and rocks near 0.15 to 0.25, rubbers approach 0.5.
Step-by-Step Solution:
Recall constraints: G = E / [2 (1 + ν)] and K = E / [3 (1 − 2 ν)].For G > 0 and K > 0 with E > 0 ⇒ 1 + ν > 0 and 1 − 2ν > 0 ⇒ ν < 0.5.Therefore, ν is less than 1 and practically less than 0.5 for standard materials.Verification / Alternative check:Empirical databases list ν for common materials well below 0.5.
Why Other Options Are Wrong:
- Greater than or equal to 1 violates stability relations.
- “Undefined” is incorrect; ν is well-defined from lateral and axial strains.
- “Negative for all metals” is false; auxetics are special cases, not typical metals.
Common Pitfalls:Assuming ν = 0.5 for all polymers; only nearly incompressible rubbers approach it, not all.
Final Answer:Less than 1