This looks like a complicated problem, which is probably why you haven't gotten any response. I do not have a solution for this, but I too would be very interested to know if this is possible. My first thought was to somehow create a "hinge" on each section and then create a coincident mate where the two parts slide together. If you set the assembly to "flexible", then the motion should simulate the opening and closing of the flexible part. Of course, the trick is to set that "hinge" mate on a circular part, and it would just be an illusion at best. /boggle
You could probably cheat something in there, but I'm certain that it would require changing the geometry of your flexible part to allow this to happen.