Lets say you want to build a bridge out of carbon fiber. This has never been never been done before, and it's super expensive stuff. So your goal is to use as little material as possible, but obviously your bridge still needs to have enough strength.
To start you look up how strong is carbon fiber, and the online data sheets tell you that a 10 oz cloth has a tensile strength of 800KSI.
After running the math this sounds perfect and should give your bridge enough strength for it's uses.
However, before you start a super expensive project that's never been done, based on nothing more than datasheets you found online and equations that might not fully apply to your material you run a sanity check.
Before you start building your full sized bridge, you build a small one that's 1/10th the size.
Assuming this small bridge is exactly the same as the large one, just using 1oz fiber instead of 10 oz fiber would your small bridge endure 1/10th the load of the full sized one?
I don't mean to apply this question to carbon fiber alone. With anything in engineering if you scale up a model perfectly using the same materials would the strength scale up proportionally, or is there some kind of real life nuance that blows all this mathematical beauty out of the water?