Elastic constants relationship check: If the modulus of elasticity E equals twice the modulus of rigidity G (i.e., E = 2G), then Poisson's ratio ν is equal to zero. Is this statement correct?

Introduction / Context:Elastic constants of isotropic materials are interrelated. Recognizing the standard relationship among E (Young's modulus), G (shear modulus), and ν (Poisson's ratio) is essential in stress–strain analysis and finite element modeling.

Given Data / Assumptions:

• Isotropic, homogeneous, linear elastic material.
• Given that E = 2G.

Concept / Approach:The standard relation for isotropic materials isE = 2 * G * (1 + ν)Rearranging gives ν = (E / (2G)) − 1. Substituting E = 2G directly yields ν = 0.

Step-by-Step Solution:

Verification / Alternative check:Typical metals have ν around 0.25 to 0.35, which would give E closer to about 2.5G to 2.7G. The special case ν = 0 indeed makes E exactly 2G, matching the provided statement.

Why Other Options Are Wrong:

• “Incorrect” conflicts with the exact algebraic relation.
• “Depends on temperature only” and “Correct only for plastics” are irrelevant; ν is determined from the relation, not material class per se.
• “Cannot be determined” is false because E = 2G fully determines ν = 0 for isotropy.

Common Pitfalls:Applying the relation to anisotropic materials (where it does not hold) or confusing true values with approximate empirical ranges for specific materials.

Final Answer:Correct