I came across a statement that whenever any stretching or compressing is done on any object, its change in volume is always greater than $0$. This means that density always decreases (mass remaining constant) or, it remains constant for purely incompressible objects but it cannot increase.

Why is that? Why can't the density of an object not increase on applying any sort of strain on it? Here is the context in which I came across it, Poisson's ratio

Edit: Chill guys, I do not study from this link or blogspot. I googled the question and got this link among the many that actually had some proof, although wrong. That's why I asked it here for clarification.

  • $\begingroup$ Can you link/show the reference were you read it? $\endgroup$ – Maxim Apr 22 '19 at 13:09
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    $\begingroup$ @Maxim Is right, you need to show where you saw this. Certainly you can compress things and increase their density... $\endgroup$ – Aaron Stevens Apr 22 '19 at 13:16
  • $\begingroup$ I read it in a different context. That, the poisson's ratio can have a maximum value of 0.5 , which comes as a consequence of putting dV≥0 $\endgroup$ – user226375 Apr 22 '19 at 13:23
  • $\begingroup$ The definition of Poisson's ratio in your reference is incorrect. There should be a minus sign. $\endgroup$ – Chet Miller Apr 22 '19 at 22:51

The link you've posted discusses what they are specifically talking about.

They are specifically referring to common "engineering" materials, which behave in standard ways where the same relationships generally apply. To rip directly from Wikipedia's Poisson's Ratio page:

The Poisson's ratio of a stable, isotropic, linear elastic material must be between −1.0 and +0.5 because of the requirement for Young's modulus, the shear modulus and bulk modulus to have positive values.

The link you provided uses similar material assumptions to show that under those assumptions, the ratio must be less than 0.5. If not, you get conflicting information, and something about your assumptions is incorrect.


Apart from been badly written and being careless with sign conventions, some of the statements in the OP's link are just nonsense.

In particular, the argument that internal strain energy is somehow equivalent to a temperature increase, and therefore materials expand in volume whether they are in compression or in tension, is frankly "so stupid it's not even wrong".

I suggest you get your information about mechanical engineering from reputable sources, and that link is not one of them.

There is no physical reason why Poisson's ratio has to be less than 0.5, and materials exist where it is greater - see for example Lee, T. and Lakes, R. S., "Anisotropic polyurethane foam with Poisson's ratio greater than 1", Journal of Materials Science , 32, 2397-2401, (1997). (link here).

  • $\begingroup$ To be fair, the link does actually state (multiple times) that it only applies to certain materials. "Hence for the general engineering materials which have positive coefficient of expansion and are isotropic in nature the Poisson's ratio is always less than 0.5." The way they reach the conclusion is pretty backwards though, since they're using the least straightforward example. I'm pretty sure you could show the same thing using much more fundamental engineering equations, which is why they got the math to work at all. Blogspot is definitely not a good learning tool though. $\endgroup$ – JMac Apr 22 '19 at 14:00
  • $\begingroup$ The material you have stated is an anisotropic one. Is the inequality true for isotropic materials? $\endgroup$ – user226375 Apr 22 '19 at 14:15

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