Folding Flat Crease Patterns With Thick Materials

Abstract

Modeling folding surfaces with nonzero thickness is of practical interest for mechanical engineering. There are many existing approaches that account for material thickness in folding applications. We propose a new systematic and broadly applicable algorithm to transform certain flatfoldable crease patterns into new crease patterns with similar folded structure but with a facetseparated folded state. We provide conditions on input crease patterns for the algorithm to produce a thickened crease pattern avoiding local selfintersection, and provide bounds for the maximum thickness that the algorithm can produce for a given input. We demonstrate these results in parameterized numerical simulations and physical models.