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

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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

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

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