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It seems that if poissions ratio is true then volume changes with stress and strain mass remaining same does that did mean density changes?

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Yes, the density changes under deformation, with the exception of some materials with volume almost constant under deformation. The most obvious change is for the gases where it it obvious that density depend on the pressure. For liquids and solids the change is much smaller but it is there. A sound wave in liquids and solids can be described as local variations in density that propagate through the material. The variation in density for solids depends on Poisson ratio by a factor of (1-2$\gamma$) where gamma is Poisson ratio. For some rubbers $\gamma$ is very close to 0.5 and the change in volume (and density) is close to zero. For common metals is around 0.3 so the change in volume and density is there even though it may be quite small.

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