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Homework Help: Why would density increase when Poisson's ratio > 0.5?

  1. Oct 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Does anyone understand why density would increase when the poisson ratio is greater than 0.5 as indicated in this slide from my professor:


    Does this density increase apply to a system undergoing tension or compression or both?
  2. jcsd
  3. Oct 19, 2012 #2

    Simon Bridge

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    You have to think about what Poisson's ration means ... how does a compression affect volume for different Poisson's Ratios?
  4. Oct 20, 2012 #3

    Alright so here calculated what the volume change would be for when Poisson's ratio < 0.5. It told me that the volume would decrease which implies that the density increases. But according to the lecture notes this is not true. Instead when the ratio is < 0.5 the density decreases...

    Note: I also calculated for the volume when Poisson's ratio = 0.5, which according to the notes there should be no volume change. But in my calculations I found there is a volume change...

    What am I doing wrong?
  5. Oct 20, 2012 #4
    Let a bar be stretched by εx. For a Poisson ratio of 0.5, the strains in the y and z directions are:

    εy=-0.5 εx

    εz=-0.5 εx

    The volumetric strain is the sum of the three linear strains, and is equal to zero.

    Same problem with Poisson ratio = 0.3

    εx + εy + εz = 0.4 εx

    So the volume increases, and the density decreases when a bar is stretched under tension and the material has a Poisson ratio of <0.5
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