What the heck is Vibranium?

Vibranium is a mythical metal that is present in the Marvel universe. It was chosen for Captain America's shield for its impressive material characteristics. It can absorb all vibrations without transferring them to the person behind the sheild

If it doesn't exist, how can we really say anything about the physics of it?

Well, we can look at the evidence we are given. In the Marvel Cinematic Universe, it is presented as being vibranium, and also withstands a massive amount of damage. In its debut scene, it takes rounds from a 9mm handgun without any appreciable damage. 

It can be assumed with how little damage the shield took that it could take a significant amount more before needing any form of repair, other than repaints.