# Why would density increase when Poisson's ratio > 0.5?

1. Oct 19, 2012

### theBEAST

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. Oct 19, 2012

### Simon Bridge

You have to think about what Poisson's ration means ... how does a compression affect volume for different Poisson's Ratios?

3. Oct 20, 2012

### theBEAST

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?

4. Oct 20, 2012

### Staff: Mentor

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