possible to model the transformation of a flat shape to a 3D form based on material characteristics?

a drawing that attempts to describe the general process that i’m in search of—a sort of reverse unfolding . . . flat-to-3D by pulling an edge of a flat shape into a new position in 3D space, resulting in a 3D model of the transformation:

https://www.dropbox.com/s/dgurtmu43ukhe30/Photo%20Apr%2016%2C%208%2049%2055%20PM.jpg?dl=0