Wheels that Won't Kill You?

How to make car wheels NOT poppable?

First of all, unless you can find some utterly indestructible elastic material to contain it, don't fill them with any kind of liquid or gas.

So...

  Make them out of some sort of solid rubber?
   would this cause too much energy loss or melting due to internal friction?
  Just put a bunch of radially oriented springs inside?
    would need multiple parts of springs with different tensile strengths to 
     absorb shocks/vibrations at various frequencies/amplitudes?
  Just have a hollow metal drum or perhaps a solid really hard rubber, and perhaps 
   with a thin layer of (softer?) rubber outside, with a sensitive suspension that 
   absorbs all the small stuff?

Or, maybe they can be gas-filled, but compartmentalized, much like with the 
 hugely successful Titanic. 
  Fill them with some sort of rubber or otherwise elastic aerogel substance?  
  Use normal tire rubber, but organized in rather large 3-d cells?  'Rather large'   
   might be 1-8 cubic inches.. just enough to mitigate damages while the tire can 
   remain flexible, not melt due to internal friction, and not be too heavy

Some of these options could call for an inner core that rarely needs replaced, but an outer rubber covering that could be replaced as needed (for treading and other wear-down) by the auto mechanic.