Question

Show that the value of Poisson's ratio is lies between-1 and 1\2.

Answer 1

An easy way of explaining this is to use the relationships between the Young's modulus EE, shear modulus GG, bulk modulus KK, and Poisson's Ratio νν.

E=2G(1+ν)=3K(1−2ν)E=2G(1+ν)=3K(1−2ν)

Now under conditions of simple tension and simple shear, all materials known experience displacements in the direction of force and increase in volume in case of hydrostatic loading. So E,GE,G and KK cannot be negative. So,

1+ν≥0⟹ν≥−11+ν≥0⟹ν≥−1

and

1−2ν≥0⟹ν≤121−2ν≥0⟹ν≤12

Combining the above,

−1≤ν≤12