I'll chime in here with half baked input!

I think you would want to make the model in moi more like michaels, a formed solid, as doing the folding in Moi would not export out very well for texturing (I'm open to being wrong here!)

Then doing the folds with displacment in the render package.

From Moi



Using displacement to get the folding.




I could have spent more time here to get a better looking fold, and possibly added a helix in moi to use as rope to hide the pinched parts.
Also, I beleive brian is an accomplished carrara user and may be able to do this better.

I used the water-waves displacement.

Burr