This question has been bothering me for over forty years. If we have a cylinder containing a low volume of a random distribution of small un-deformable particles (which approximate to points), and we strain the cylinder so that its length increases by (say) 50% while its volume remains constant, will the distribution of particles still be random?

If not, can the degree of non-randomness be measured?

Can the strain be deduced from this measure of non-randomness?

The 2D version of this question is slightly simpler.

In this case we start with an area containing a random distribution of points. We then elongate the area by (say) 50% assuming the area remains constant.

Is the distribution of points still random? If not can the degree of non randomness be measured? Can the strain be deduced from the latter measurement?

The answer would be relevant to metallurgy and physics of solids.

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