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If you have two metal springs that are coiled in the same way, but one is twice the length of the other, the spring constant will be half as large for the longer one. That makes sense of course.

What's the quantity that's invariant over rest-length called? I guess it would be $\delta=\frac{k}{x}$, but I'm just wondering the name.

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The stiffness of solids can be characterized by three different elastic moduli, all material properties: the Young's elastic modulus, the shear modulus, and the bulk modulus. All are approximately in the tens or hundreds of GPa. The Young's elastic modulus is convenient to use when stretching long, thin samples. The shear modulus is of interest because shear is what ultimately leads to failure in ductile materials such as metal. The bulk modulus measures the compressive resistance to a uniform surrounding pressure.

In any case, all three are intrinsic material properties that would be identical for any two springs made of the same polycrystalline metal, regardless of their size. Is this what you were looking for?

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  • $\begingroup$ Yeah, thank you. I was just thinking in terms of a line-spring, so young's elastic modulus is what I was looking for. $\endgroup$
    – Sam Bobel
    May 2, 2018 at 2:10

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