Poisson's ratio is defined as?

Poisson's ratio is defined as?

• A. the ratio of the proportional decrease in a lateral measurement to the proportional increase in length in a sample of material that is elastically stretched
• B. the ratio of the proportional increase in a lateral measurement to the proportional decrease in length in a sample of material that is elastically stretched
• C. the ratio of the volumetric strain to the axial strain
• D. the ratio of the shear strain to the axial strain

Answer: (B)

Poisson's ratio describes how a material's dimensions change perpendicular to the direction of loading when it is stretched (or compressed) along its length. When you pull a specimen in one direction, it tends to get thinner in the other directions. The standard definition is the negative ratio of the transverse (lateral) strain to the axial (longitudinal) strain, which is the magnitude of how much the material contracts laterally divided by how much it stretches axially. Because a stretch causes the length to increase and the width/height to decrease, the ratio of the lateral contraction to the axial extension corresponds to Poisson's ratio. In other words, Poisson's ratio is best described as the proportional decrease in a lateral dimension relative to the proportional increase in length. The other options don’t fit this relationship: relating volumetric strain to axial strain isn’t Poisson’s ratio, relating shear strain to axial strain isn’t it either, and describing lateral expansion with axial contraction would imply behavior opposite to typical uniaxial tension in most materials.

Poisson's ratio describes how a material's dimensions change perpendicular to the direction of loading when it is stretched (or compressed) along its length. When you pull a specimen in one direction, it tends to get thinner in the other directions. The standard definition is the negative ratio of the transverse (lateral) strain to the axial (longitudinal) strain, which is the magnitude of how much the material contracts laterally divided by how much it stretches axially.

Because a stretch causes the length to increase and the width/height to decrease, the ratio of the lateral contraction to the axial extension corresponds to Poisson's ratio. In other words, Poisson's ratio is best described as the proportional decrease in a lateral dimension relative to the proportional increase in length.

The other options don’t fit this relationship: relating volumetric strain to axial strain isn’t Poisson’s ratio, relating shear strain to axial strain isn’t it either, and describing lateral expansion with axial contraction would imply behavior opposite to typical uniaxial tension in most materials.