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If I have a cylinder made of, lets say steel. Steel has a Poisson's ratio of roughly 0.33. The cylinder is restrained in the vertical direction so no displacement can occur.

If I apply an internal pressure to the cylinder, it is going to expand laterally, but it cant in the vertical direction because it is restrained.

Seeing as the Poisson ratio is a ratio of lateral to longitudinal strains and the strain in the longitudinal direction will be zero, where does that leave the poisson ratio? If The longitudinal strain is zero, you cannot divide the lateral strain by zero!

Am I missing something?