Animate a UV unwrapped plane bending I want to take a flat plane and animate one end of it rolling up to a roughly 90 degree angle.
The plane is UV unwrapped with a repeating texture and needs the distortion to be minimal.
This image roughly shows the before and after of what I'm wanting to accomplish.

blend file: 
Initially, I tried using the curve modifier with a shape key on the curve but I was having issue with the plane sliding around.
Please let me know if there's any other info I can provide to clarify.
Extend your curve a bit in Edit mode so that its 2 ends go a bit further and instead of creating shapekeys, just move your curve on the Y axis: