Elastic constants relationship: For a material with Poisson’s ratio ν = 0.4, what is the ratio of shear modulus to Young’s modulus (G/E)?

Introduction / Context:In isotropic linear elasticity, the independent constants E (Young’s modulus), G (shear modulus), and ν (Poisson’s ratio) are linked. Converting between them is routine in strength of materials and finite element modeling.

Given Data / Assumptions:

• Isotropic, homogeneous material.
• Poisson’s ratio ν = 0.4.
• Standard elastic relation G = E / [2 * (1 + ν)].

Concept / Approach:Use the canonical relationship connecting E, G, and ν. Substituting ν directly gives the ratio without needing absolute values of E or G.

Step-by-Step Solution:

Verification / Alternative check:Sanity check: For ν between 0 and 0.5, G/E should lie between 1/3 and 1/2.8; 5/14 ≈ 0.357 fits the expected range.

Why Other Options Are Wrong:

• 5/7, 7/5, 14/5 are greater than 1, impossible for G/E with ν = 0.4.
• 2/5 = 0.4 does not match the exact relation for ν = 0.4.

Common Pitfalls:Forgetting the 2 in the denominator; confusing G/E with E/G; using an incorrect ν value range that yields nonphysical ratios.

Final Answer:5/14