Mechanical Properties Of Solids

Given that the material has a Poisson's ratio is and the longitudinal strain of . Now the Poisson's ratio is defined as

where is the resulting Poisson's ratio, is transverse strain [negative for axial tension (stretching), positive for axial compression] is axial strain (positive for axial tension, negative for axial compression). Thus there is no change in volume.

Let the initial length of the metal wire is .
The strain at tension is
The strain at tension is
Suppose, the Young's modulus of the wire is , then

where, is an cross-section of the wire. assume to be same at all the situations.

Stress, of
But Young's modulus,
putting

Poisson's ratio,


Change in volume,