In all probability the strongest material that can actually exist would be perfect carbon nanotubules. (I’m uncertain if perfect nanocrystals of beryllium would have a slightly better strength/weight ratio). But let’s say there was such a material as Unobtainium, consisting of stabalized quark chains or some such, which had 90% of it’s entire mass consisting of binding energy. Let’s say we had a piece of Unobtainium of whatever thickness would give it a mass of one kilogram per meter of length. How strong would it be? I can calculate E=MC[sup]2[/sup], but I don’t know how to relate energy to force (breaking strain of cable) in this case.
Scrith?
Sorry, got nothing else, but somebody is going to blurt out “Scrith”, so it might as well be me.
What?
Scrith is the material that Ringworld is made of in the Larry Niven novels. It can’t recall the calculations, but imagine a taking all the material in the solar system and pressing it into a giant ring apprpximately the same size as Earth’s orbit, putting the sun in the center, and then spinning it up to generate artificial gravity on the inside of the ring. Throw in some other details like thousand mile walls around the inner edges of the ring to hold in an atmosphere, and you have a liveable environment with earth-like conditions, but about a million times the surface area.
I highly reccommend the books if you like to ponder questions about engineering on a truly monumental scale.
For a slowly growing crack in a brittle material, the rate of work done by a force extending a crack equals the rate of increase in (strain energy plus the energy of the newly created surfaces). This is the basis of fracture mechanics. The change in strain energy can be determined by solving a boundary value problem for a given stress-strain law and boundary conditions corresponding to the loading geometry you are interested in. Surface energy has been calculated and measured for several pure compounds, so in principle you could do it for any imaginary material you wanted to concoct.
That approach will let you relate force to crack length, and you can decide how long a crack you can tolerate before calling it a failure, or you can define failure as unstable crack growth. However, failure theories developed along these lines tend not to work very well for real materials, because of inhomogeneities, plastic deformation, and other factors. Then again, there is no universal failure theory for any material, so maybe that is not too much of a shortcoming.