When sheet of paper is folded along a closed curve, it buckles dramatically. When cut, it collapses and lies flat. We have developed a mechanical model to explain the shape of an elastic sheet folded along a curve that incorporates the geometric frustration inherent in the folded structure. As the curved fold becomes wider, geometrical effects play a more prominent role. The buckled shapes become more rigid to avoid stretching within the sheets on either side of the fold.
M.A. Dias, L. Dudte, L. Mahadevan, and C.D. Santangelo, “Geometric mechanics of curved crease origami”, Phys. Rev. Lett. 109, 114301 (2012). [JOURNAL] [ARXIV].