# Stress-strain relation in insane proportions

We have: $$\sigma = E \epsilon$$ and $$\epsilon = \Delta L/L_0$$. This seems to imply that for a constant strain, we will achieve a proportional change in length.

However, it doesn't rest well with me that this relation is not dependent on $$L_0$$. For instance, say I have some material that has an $$E = 1$$ MPa and an area of $$1$$ m$$^2$$, and I put a $$1$$ N force on it. Then it would have a strain of $$\epsilon = 1\times 10^{-9}$$.

So if my bar is 1m long, then there would be a millimetre's difference in the length. But if my bar was in space and a kilometre long, then would I expect to see the bar shrink by a full metre?

Or do I have an overly simplistic understanding of stress and strain?

• $E$ is usually in hundreds of GPa so your value isn't realistic at all. – John Alexiou Sep 6 '20 at 1:12