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If you stretch an object, each side changes length by an amount due to strain,e, so the new length is L(1+e)..Each side normal to the stretch direction contracts by an amount equal to poisson ratio x the stretch.

If you calculate the change in volume V you get

dV = Ve(1-2u)

Ay u = 0.5 there is no volume change (incompressible); if it were greater than 0.5 volume would decrease which is unlikely. If it is 0, there is no lateral contraction and volume increases. If less than 0 the object will actually expand laterally rather than contract, and some special materials do this. Poisson ratio can be as low as -1, but most common materials lie between 0 and 0.5

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