One possible way would be to mimic the human penis, by including small flexible tubing in the polymer, with the tubes attached to a very small pump. Touch the switch, how big do you want it to grow? The liquid medium could be water, glycerine, etc or air, nitrogen, argon, etc. Sort of like a blood cuff. Another way would be to use a polymer that absorbs water, briefly immerse the polymer and watch it swell. It might be possible to make the polymer as you suggested by using a liquid crystal polymer which responds to changes in touch, temperature, etc. What ratio of growth to original volume are you looking for?
Are you familiar with heat shrinkable sleeving used in electronics? It's heated, expanded over a mandrel and cooled. Then it's slipped over the wire, heated and it shrinks back to as near it's original size as allowed.
Perhaps there's a way to reverse this process. Shrink the stent, insert it and some combination of body heat/chemistry/electrical impulse will cause it to expand.