Poisson's Ratio for a Perfectly Incompressible Linear Elastic Material

In the field of mechanics and material science, Poisson's ratio is a dimensionless quantity that describes the response of a material to applied forces. It is defined as the ratio of lateral strain to axial strain when a material is subjected to uniaxial stress. Poisson's ratio is denoted by the Greek letter ν (nu).

Explanation:
Poisson's ratio is a measure of the deformation that occurs in a material when it is subjected to an external force. It relates the change in transverse strain (lateral strain) to the change in axial strain (longitudinal strain).

For a perfectly incompressible material, the Poisson's ratio is 0.5. This means that when a force is applied to the material, the material will not change its volume but will only deform in the lateral direction.

Perfectly Incompressible Material:
A perfectly incompressible material is an idealized concept where the volume of the material remains constant regardless of the applied forces. In reality, no material is perfectly incompressible, but some materials, such as liquids and certain rubbers, have very high bulk moduli and can be considered nearly incompressible for certain applications.

Interpretation of Poisson's Ratio:
Poisson's ratio can range from -1 to 0.5. A positive value indicates that the material contracts laterally when stretched axially, while a negative value indicates that the material expands laterally when stretched axially.

When Poisson's ratio is 0, it indicates that the material is incompressible and does not deform laterally when subjected to axial stress. In this case, the material only experiences axial strain, and there is no change in volume.

In the case of a perfectly incompressible material, Poisson's ratio is 0.5. This means that when the material is subjected to axial stress, it will deform equally in all directions, maintaining its volume constant. The material will not change its shape or size, but only deform laterally.

To summarize, the correct answer to the given question is option 'B' (0.5) because for a perfectly incompressible linear elastic material, the Poisson's ratio is 0.5.

0.5