Bending maintaining Size

I have to simulate a sheet of paper warping around a cylinder and sliding through some slots; the correctness of measures is important, so the paper must mantain his sizes when bending, and it should adapt his own shape while marching through, and while the cylinder spins. This sheet should actually be driven by the cylinder.
How can achieve this?
The Simple Deform modifier is useless in this case, and so is for the Curve modifier.

Any help would be very appreciated.
Thanks in advance,


Edit: I solved with the Curve modifier, I don’t know why it didn’t worked the first time.