I have done some problems in current electricity where you stretch or squeeze a wire, the length and area of cross section change but the volume remains same.

A question on math.stackexchange.com tries to answer it mathematically( https://math.stackexchange.com/questions/1125781/does-the-volume-of-a-ball-remain-constant-under-deformation)

But why it is thee physical reason behind volume being unchanged and on what physical limits the stretching & squeezing (and other sort of deformation) will leave the volume unchanged?

P.S. As per Mike Dunlavey's comment I am not talking about incompressible objects.

  • $\begingroup$ Ever heard of something being "incompressible"? $\endgroup$ – Mike Dunlavey Sep 17 '16 at 0:34
  • $\begingroup$ Yes! But I am thinking about non-incompressible objects. And your comment does not answer my question. $\endgroup$ – Mockingbird Sep 17 '16 at 1:02
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    $\begingroup$ If the object is compressible, the volume can change when deformed. $\endgroup$ – garyp Sep 17 '16 at 2:55
  • $\begingroup$ Constancy of volume or its opposite, is an assumption you make, and which subsequently needs to be verified experimentally. $\endgroup$ – Deep Sep 17 '16 at 5:53

There are no truly incompressible materials; it is possible to measure the compressibility (or its inverse, the 'bulk modulus') of any solid, liquid, or gas.

As to why a (for instance) copper wire might stretch but retain the same volume, it is because copper is ductile. The metal can be deformed to a large extent without causing gross structural damage (like microcracks), and without recrystallizing into a form that has fewer atoms per cubic millimeter.

At elevated temperatures, unless oxidation or other contamination takes place, metals will 'anneal' and heal microscopic damage. For example, copper wire is drawn thin by pulling through a sequence of narrow orifices, then annealing the 'hard drawn' result back to soft copper. The 'hard drawn' worked copper, because of internal strain, may differ slightly from the annealed (normal) copper in density, but in my experience this effect is always dismissed as negligible.

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  • $\begingroup$ Are you saying that the Poisson ratio of copper is very close to 1/2? $\endgroup$ – Chet Miller Sep 17 '16 at 11:23
  • $\begingroup$ And what will apply to liquids? Why'd they also want to keep volume same under some kind of strain? $\endgroup$ – Mockingbird Sep 17 '16 at 16:28
  • $\begingroup$ Poisson's ratio for copper is 0.355; that only applies to elastic stress, not to stretching and deformation. The elastic response is slight in copper (we $\endgroup$ – Whit3rd Sep 17 '16 at 23:42
  • $\begingroup$ ..don't make springs of copper). It stretches nicely, though. $\endgroup$ – Whit3rd Sep 17 '16 at 23:48

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