Which statement defines Poisson's ratio?

Which statement defines Poisson's ratio?

• 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 axial strain
• D. the ratio of the shear strain to axial strain

Answer: (C)

Poisson's ratio describes how a material deforms in directions perpendicular to an applied load. When you stretch along one axis, the material typically contracts in the transverse directions, and the ratio of that lateral (transverse) strain to the axial (longitudinal) strain, with a minus sign, defines Poisson's ratio: ν = - ε_transverse / ε_axial. The minus sign is used so ν is positive for most common materials (usually between 0 and 0.5). A handy way to connect this to volume is to recall that for uniaxial tension, the transverse strains are ε_y = ε_z = -ν ε_x. The resulting volumetric strain is ΔV/V = ε_x + ε_y + ε_z = (1 - 2ν) ε_x, so the ratio of volumetric to axial strain equals 1 - 2ν. This shows why the ratio of volumetric strain to axial strain is related to ν, but it is not the definition of Poisson's ratio itself.

Poisson's ratio describes how a material deforms in directions perpendicular to an applied load. When you stretch along one axis, the material typically contracts in the transverse directions, and the ratio of that lateral (transverse) strain to the axial (longitudinal) strain, with a minus sign, defines Poisson's ratio: ν = - ε_transverse / ε_axial. The minus sign is used so ν is positive for most common materials (usually between 0 and 0.5).

A handy way to connect this to volume is to recall that for uniaxial tension, the transverse strains are ε_y = ε_z = -ν ε_x. The resulting volumetric strain is ΔV/V = ε_x + ε_y + ε_z = (1 - 2ν) ε_x, so the ratio of volumetric to axial strain equals 1 - 2ν. This shows why the ratio of volumetric strain to axial strain is related to ν, but it is not the definition of Poisson's ratio itself.