Elastic constants – quick evaluation:\nFor an isotropic material with Poisson’s ratio v = 0.25, what is the ratio of bulk modulus to Young’s modulus (K / E)?

Introduction / Context:
Bulk modulus K and Young’s modulus E are two fundamental elastic constants for isotropic materials. Knowing how they relate through Poisson’s ratio v allows quick conversions between laboratory test data and design parameters. This question checks your fluency with the standard isotropic elasticity relations.

Given Data / Assumptions:

• Material is homogeneous and isotropic.
• Poisson’s ratio v = 0.25 (dimensionless).
• Small-strain linear elasticity applies.

Concept / Approach:
The well-known relation between E, K, and v in isotropy is K = E / (3 * (1 − 2v)). Rearranging gives K / E = 1 / (3 * (1 − 2v)). Substituting v immediately yields the numerical ratio without unit conversions, because both K and E have identical dimensions (stress).

Step-by-Step Solution:

Verification / Alternative check:
Use the companion identity E = 3 * K * (1 − 2v). Solving for K / E provides the same expression. For v in the common metallic range (0.25 to 0.35), K is typically of the same order as E, which is consistent with 2/3 for v = 0.25.

Why Other Options Are Wrong:

• 1/3 or 1/2: arise from omitting the factor (1 − 2v) or misapplying the 3.
• 1: would require v = 0, which is not the case.
• 3/2: inverted relationship; not physically consistent.

Common Pitfalls:
Confusing the E–K relation with E–G (E = 2 * G * (1 + v)). Always check which modulus is in the formula and keep track of the 3 and (1 − 2v) factors.

Final Answer:
2/3