Home » Civil Engineering » Strength of Materials

Poisson’s ratio — general bound For stable, common engineering materials, the numerical value of Poisson’s ratio ν is generally:

Difficulty: Easy

Greater than 1
Less than 1
Exactly equal to 1
Undefined for solids
Negative for all metals

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.

Poisson’s ratio — general bound For stable, common engineering materials, the numerical value of Poisson’s ratio ν is generally:

More Questions from Strength of Materials

Discussion & Comments