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The Poisson's ratio for a perfectly incompressible linear elastic material is

  1. $1$
  2. $0.5$
  3. $0$
  4. Infinity
in Applied Mechanics and Design 24.6k points
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For a perfectly incompressible linear elastic material, the change in volume when stretching is zero or the volume remains constant. When a sample of material is stretched in one direction, it tends to get thinner in the other two directions. Poisson's ratio (ν, μ), named after Simeon Poisson, is a measure of this tendency. Poisson's ratio is the ratio of the relative contraction strain, or

$Poisson's ~Ratio = \frac {Transverse~strain (normal~to~the~applied~load)}{relative~extension~strain (in~the~direction~of~the ~applied~load)}$

Therefore, the answer is $0.5$ i.e. Option $B$.
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