Elastic constants conversion: a material has Young’s modulus E = 125 GPa and Poisson’s ratio ν = 0.25. What is its modulus of rigidity C (shear modulus G)?

Introduction / Context:Converting between elastic constants is a routine task in design and analysis. Knowing any two of E, ν, C (G), and K allows you to compute the others for an isotropic material.

Given Data / Assumptions:

• E = 125 GPa.
• ν = 0.25.
• Isotropic, linear-elastic behavior.

Concept / Approach:Use the identity relating E, ν, and C: C = E / (2 * (1 + ν)). This comes directly from isotropic elasticity theory.

Step-by-Step Solution:

Verification / Alternative check:Cross-check with the inverse formula E = 2C(1 + ν). With C = 50 GPa and ν = 0.25, E = 2 * 50 * 1.25 = 125 GPa, which matches the given value.

Why Other Options Are Wrong:30, 80, 100, 62.5 GPa do not satisfy C = E / (2 * (1 + ν)) for the provided E and ν.

Common Pitfalls:Plugging ν into a bulk-modulus relation by mistake, or forgetting the factor (1 + ν) in the denominator.

Final Answer:

50 GPa