[ElCid]

I'm looking to make a knee pad but I want a material that's like a rubber and a gel that when I fall down on my knee it will take the full impact and bounce back, even if it bounces me back on my feet. I'm thinking some type of polymer with high elasticity but I've run up a wall looking for options and it dawned on me that something like this might not even exist. Is there a material like this currently and is it even possible to synthesize something like this?

[Meter]

You are essentially asking for a material which will conserve the majority of the potential energy you close when you fall over. Something like it might exist, but I doubt it would work for your purposes or be (at all) affordable.

[Enthalpy]

First attempt: elastomer that bounce back. The best is natural rubber. Some artificial rubbers do bounce, others absorb. Foams help where rubbers are too hard.

What I dislike: if you fall from 0.5m and rebound over 0.05m you get >10g, rather 20g or more, fed by your knees, so you're hurt.

Second attempt: feed some deformable envelope with a pressured gas, for instance air, like many bouncing balls are made, and also tyres: tennis, soccer, basket balls. More elastic, lighter, cheaper. You can build your thingy thicker for a less hard shock. But don't expect miracles.

A deformable envelope often means fibres in an elastomer, possibly with two envelopes in an other like many tyres have, and a valve for inflating. Consider existing hardware like bicycle inner tubes, fit it in a shell.