Question

If Poisson's ratio $\sigma$ for a material is $-\frac{1}{2}$, then the material is

• A. Elastic fatigue
• B. Incompressible
• C. Compressible
• D. None of the above

Answer 1

The correct option is B Incompressible

We know that compressibility,
$C=\frac{1}{K}$
Also, $\frac{dV}{V}=(1+2\sigma )\frac{dL}{L}$
Given, $\sigma =-\frac{1}{2}$, then $\frac{dV}{V}=0$
i.e., volume is Constant
or $k=\infty$ i.e., the material is incompressible.