Question

For a tissue with Young's modulus 4 kPa and shear modulus 1.5 kPa, what is the value of the Poisson's ratio?

• A. \(\frac{1}{4}\)
• B. \(\frac{1}{5}\)
• C. \(\frac{1}{2}\)
• D. \(\frac{1}{3}\)

Hint:

Memorize the key relationships between elastic moduli for isotropic materials: \(E = 2G(1 + \nu)\) and \(E = 3K(1 - 2\nu)\), where K is the bulk modulus.

Answer 1

The Correct Option is D

Step 1: Concept:
For an isotropic and linear elastic material, Young’s modulus ($E$), shear modulus ($G$), and Poisson’s ratio ($\nu$) are related by: \[ E = 2G(1 + \nu) \]
Step 2: Substituting Given Values:

• $E = 4$ kPa
• $G = 1.5$ kPa

\[ 4 = 2 \times 1.5 \times (1 + \nu) \] \[ 4 = 3(1 + \nu) \]
Step 3: Solving for Poisson’s Ratio: \[ 1 + \nu = \frac{4}{3} \] \[ \nu = \frac{4}{3} - 1 = \frac{1}{3} \] Final Answer: The Poisson’s ratio of the tissue is $\frac{1}{3}$.