# Finding Poisson's ratio of 3D model in ANSYS

I want to find the Poisson's ratio of a 3D model, not the material but the model. How can I do this in ANSYS workbench?

I am using this formula, but I can't get it to work with different models. I am not sure what strain is the correct to use, can someone point me in the correct direction?

$$\nu=-\frac{\text{Strain in direction of load}}{\text{Strain at right angle of load}}$$

$$\nu=-\frac{\varepsilon_{lateral}}{\varepsilon_{axial}}$$

• whatever you are calculating you should not call it poison's ratio as that will just confuse people (unless this is a cell in a periodic structure in which case you should say so) – agentp Apr 17 '18 at 22:13
• @agentp From wikipedia: Poisson's ratio is the negative of the ratio of (signed) transverse strain to (signed) axial strain. For small values of these changes, \nu is the amount of transversal expansion divided by the amount of axial compression. (So I thinks it's fine to call it that) – Niklas Apr 18 '18 at 6:33
• These structures are not isotropic and will have different Poisson's ratios in different directions. I suggest you look at how homogenization of auxetic structures have been done in the past. There is a large amount of literature on the topic. – Biswajit Banerjee Apr 18 '18 at 8:15
• Thanks, @BiswajitBanerjee. I will look at that, but do you have any suggestions on how to measure across all kinds of models the best design? Det design is supposed to tackle load and compress then expand again when the load is removed, and I need to measure which design works best. – Niklas Apr 18 '18 at 8:28
• it is a material property and a glaring omission on the wiki page that they fail to say that in the opening paragraph. – agentp Apr 18 '18 at 11:41

## 2 Answers

Are you asking which of the two equations you give to use? In the context of a continuous material, the first one is flipped; the second is correct. However, since you're trying to apply a materials concept to a distributed structure, you can't use the strain that ANSYS will output, because this will be the material strain. Better to use $$\nu=-\frac{\frac{\mathrm{displacement\; between\; two\; points\;A\;and\;B\;spaced\;at\;a\;right\;angle\;to\;the\;load}}{\mathrm{original\;distance\; between\; points\;A\; and\;B}}}{\frac{\mathrm{displacement\; between\; the\;two\; points\;of\;load\;application\;C\;and\;D}}{\mathrm{original\;distance\; between\; points\;C\;and\;D}}}$$

• Where would i measure in the second model to get good results? Just the middle x and z axis with a vertex? – Niklas Apr 18 '18 at 5:50
• directional deformation, height: 20.809 width: 20 v=1.115541386, what am I doing wrong? – Niklas Apr 18 '18 at 6:05
• Poisson's ratio isn't defined well when applied to an arbitrary structure as described above. It's dependent on the loading and the location on the material, and it can vary between $-\infty$ and $\infty$, which is considerably different from the case of a stable continuous material, in which it is bounded by -1 and 0.5. – Chemomechanics Apr 18 '18 at 6:39
• so how would you best sett numbers to structures depending on how well they tackle a load. I am designing composite materials that compress without major damage when a load is applied, and need to test which design works best. – Niklas Apr 18 '18 at 8:10
• I can't really understand what you're asking ("sett numbers to structures"?). Maybe you could try posting another question with more detail. – Chemomechanics Apr 18 '18 at 20:23

Compute the wave velocity in a 3.05-m-diameter steel penstock having a wall thickness of 25 mm if it: i. is embedded in a concrete dam; ii. is anchored at the upstream end; and iii. has expansion joints throughout its length.