Question

For a tissue with Young’s modulus of \(3.6\ \text{kPa}\) and Poisson’s ratio of \(0.2\), what is the value of its shear modulus (in kPa)? (Round off the answer to one decimal place.)

Hint:

For isotropic linear materials: \(E=2G(1+\nu)\) and \(E=3K(1-2\nu)\). These let you convert among \(E\), \(G\) (shear), \(K\) (bulk), and \(\nu\).

Answer 1

Correct Answer: 1.5

Step 1: Use the isotropic elasticity relation between Young’s modulus \(E\), shear modulus \(G\) and Poisson’s ratio \(\nu\): \[ G=\frac{E}{2(1+\nu)}. \] Step 2: Substitute \(E=3.6\ \text{kPa}\) and \(\nu=0.2\): \[ G=\frac{3.6}{2(1+0.2)}=\frac{3.6}{2.4}=1.5\ \text{kPa}. \] Thus, the shear modulus is \(\boxed{1.5\ \text{kPa}}\).