For a material with Young’s modulus E = 200 GN/m² and modulus of rigidity G = 80 GN/m², what is the value of Poisson’s ratio (μ)?

Introduction / Context:Poisson’s ratio is a key elastic constant that relates lateral strain to longitudinal strain in materials. It can be derived from the relationship between Young’s modulus (E) and shear modulus (G).

Given Data / Assumptions:

• E = 200 GN/m².
• G = 80 GN/m².
• Isotropic, homogeneous, linearly elastic material.

Concept / Approach:The relation between E, G, and μ is:E = 2 * G * (1 + μ) Rearranging: μ = (E / (2 * G)) - 1

Step-by-Step Solution:μ = (200 / (2 * 80)) - 1= (200 / 160) - 1= 1.25 - 1= 0.25

Verification / Alternative check:Cross-check using bulk modulus relation: E = 3K(1 - 2μ). Substituting μ = 0.25 maintains consistency for isotropic elasticity.

Why Other Options Are Wrong:

• 0.15, 0.20: underestimate value.
• 0.30, 0.40: overestimate value.

Common Pitfalls:

• Using wrong formula (mixing with bulk modulus relation).
• Incorrect unit handling (ensure consistency in GN/m²).

Final Answer:0.25