Geometric mechanics of thin sheets with cuts and folds

The presence of cuts and creases in thin planar sheets can dramatically alter their mechanical and geometrical response to loading. To quantify this, we perform numerical experiments to characterize the geometric mechanics of sheets as a function of the number, size and orientation of cuts and creases. We show that the mechanical behavior of these sheets with one or a few cuts or creases can be understood in terms of simple scaling-laws, while the geometry of the deformed sheets can be approximated via a composition of simple developable units - flats, cylinders and cones - in the small and large deformation limit. We conclude by generalizing the results to characterize the geometric mechanics of sheets with more complex distributions of cuts and creases.