A wire is stretched so that its longitudinal strain is ε. Its Poisson ratio is ν. For small deformation, what is the approximate volume strain of the wire?
Options

Question

A wire is stretched so that its longitudinal strain is ε. Its Poisson ratio is ν. For small deformation, what is the approximate volume strain of the wire?

G1 Physics · Accepted Answer

Longitudinal strain is ε(longitudinal) = ε. Each transverse strain is ε(transverse) = −νε. For small strains, volume strain is the sum of the three mutually perpendicular normal strains: ε(volume) = ε −νε −νε. Therefore, ε(volume) = ε(1−2ν). Correct option: C.