vacuum forming/thermoforming elastic materials?
I'm not aware of any flexible rubbers which can be formed by vacuforming.  In my experience, when you start with a flat sheet of flexible rubber and press it against a mold, it pretty much returns to being a flat sheet of rubber when the pressure is released.

You can however cast flexible rubber (in liquid form) into a mold with your desired hollow hemisphere shape and then let it cure in the mold.  This will result in your hemisphere being the natural shape of the rubber to which it will return after each deformation.  

You will want to use a two part mold (one part to provide the outer shape of the bowl and the other to occupy the hollow interior while the foam is curing).  Two nesting bowls can be used together as the mold with the difference in the bowl sizes defining the wall thickness of your final rubber part.