What’s the maximum energy density of a spring? What material is best?
As you put more and more energy into a spring, eventually you will break it. The properties of the spring material put a limit on how much energy you can store in the material before you break it.
Typically the relevant numbers are yield stress (or elastic limit) and some kind of modulus of stiffness. Some springs are stressed in shear (like a torsion bar in torsion, or a coil spring in compression or tension), while others are stressed in tension or compression, like the surfaces of a leaf spring or a bow.
Common geometries, like the torsion bar, coil spring, or leaf spring, have a zero-stress region in the middle of the material, with stress increasing linearly up to the surface, where it is at a maximum. This geometry reduces the spring’s energy density to half of the theoretical maximum for the material. Other geometries, such as tubular torsion bars or I-beam leaf springs, can reduce the wasted weight. Springs stressed in pure compression, like a squeezed block of rubber, or in pure tension, like a stretched wire, do not have this problem.
https://en.wikipedia.org/wiki/Shear_modulus say:
The shear modulus is one of several quantities for measuring the stiffness of materials. All of them arise in the generalized Hooke's law:
- Young's modulus describes the material's response to uniaxial stress (like pulling on the ends of a wire or putting a weight on top of a column),
- the bulk modulus describes the material's response to uniform pressure (like the pressure at the bottom of the ocean or a deep swimming pool)
- the shear modulus describes the material's response to shear stress (like cutting it with dull scissors).
It also gives a table:
| Material | Typical values for |
| | shear modulus (GPa) |
| | (at room temperature) |
| Diamond[2] | 478.0 |
| Steel[3] | 79.3 |
| Copper[4] | 44.7 |
| Titanium[3] | 41.4 |
| Glass[3] | 26.2 |
| Aluminium[3] | 25.5 |
| Polyethylene[3] | 0.117 |
| Rubber[5] | 0.0006 |
http://www.freebase.com/base/materials/solid_material/shear_modulus?instances= has 13 values for the shear modulus that are totally useless because they have no attribution and no units. (Also, they have no precision.)
http://www.engineeringtoolbox.com/modulus-rigidity-d_946.html gives these values:
| Material | Shear Modulus | |
| | - G - | |
| | (10⁶ psi) | (GPa) |
| Aluminum Alloys | 3.9 | 27 |
| Aluminum, 6061-T6 | 3.8 | 24 |
| Aluminum, 2024-T4 | 4.0 | 28 |
| Beryllium Copper | 6.9 | 48 |
| Brass | 5.8 | 40 |
| Bronze | 6.5 | 44.8 |
| Cadmium | | 19 |
| Carbon Steel | 11.2 | 77 |
| Cast Iron | 5.9 | 41 |
| Chromium | | 115 |
| Concrete | 3.0 | 21 |
| Copper | 6.5 | 45 |
| Glass | | 26.2 |
| Glass, 96% silica | 2.8 | 19 |
| Inconel | 11.5 | 79 |
| Iron, Ductile | 9.1 - 9.6 | 63 - 66 |
| Iron, Malleable | 9.3 | 64 |
| Kevlar | 2.8 | 19 |
| Lead | 1.9 | 13.1 |
| Magnesium | 2.4 | 16.5 |
| Molybdenum | 17.1 | 118 |
| Monel metal | 9.6 | 66 |
| Nickel Silver | 6.9 | 48 |
| Nickel Steel | 11.0 | 76 |
| Nylon | 0.59 | 4.1 |
| Phosphor Bronze | 5.9 | 41 |
| Plywood | 0.09 | 0.62 |
| Polycarbonate | 0.33 | 2.3 |
| Polyethylene | | 0.12 |
| Rubber | | 0.0003 |
| Structural Steel | 11.5 | 79.3 |
| Stainless Steel | 11.2 | 77.2 |
| Steel, Cast | 11.3 | 78 |
| Steel, Cold-rolled | 10.9 | 75 |
| Tin | | 18 |
| Titanium, Grade 2 | 5.9 | 41 |
| Titanium, Grade 5 | 5.9 | 41 |
| Titanium, 10% Vanadium | 6.1 | 42 |
| Tungsten | | 161 |
| Wood, Douglas Fir | 1.9 | 13 |
| Zinc | | 43 |
| Z-nickel | 11 | 76 |
(See also You can stuff a UHMWPE hammock in your wallet.)
The number I was looking for is called the “specific energy” or “elastic potential energy per unit volume”.