I am not aware of any algorithm for modeling a crumpled paper, but I would surmise that you will find something relevant in the domain of the Brouwer Fix Point Theorem.
There are extensive models for 2-dimensional manifold manipulation, such as modeling waving flags, etc. For example: http://web.eng.ucsd.edu/~sgls/jfm617_1.pdf
I am not so sure of such algorithms. However since crumpled paper will have lines of weaknesses along which it crumbles then fractals analysis will suffice.