Geometric mechanics of curved crease origami

Physical Review Letters

Volumn 109, Issue 11, 2012, Pages

  Dias, Marcelo A ^a   Dudte, Levi H ^b   Mahadevan, L ^c   Santangelo, Christian D ^a  

^a UNIVERSITY OF MASSACHUSETTS   (United States)

^b HARVARD UNIVERSITY   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BROKEN SYMMETRY; CIRCULAR STRIPS; CONSTANT CURVATURE; DEFORMED STATE; GEOMETRIC MECHANICS; GEOMETRICAL FRUSTRATIONS;

ASYMPTOTIC ANALYSIS; MECHANICAL PROPERTIES;

TORSIONAL STRESS;

EID: 84866316680     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.109.114301     Document Type: Article

References (21)

1. K. Miura, in Method of Packing and Deployment of Large Membranes in Space (The Institute of Space and Astronautical Science, 1980).
2. E. Demaine and P. ORourke, Geometric Folding Algorithms (Cambridge University, Cambridge, England, 2009).
3. E. Hawkes, B. An, N.M. Benbernou, H. Tanaka, S. Kim, E.D. Demaine, D. Rus, and R.J. Wood, Proc. Natl. Acad. Sci. U.S.A. 107, 12441 (2010). PNASA6 0027-8424 10.1073/pnas.0914069107
4. M. Schenk and S.D. Guest, in Origami Folding: A Structural Engineering Approach, Origami 5, edited by, Mark Yim, (A K Peters Ltd, Wellesley, MA, 2011).
5. H.M. Wingler, Bauhaus: Weimar, Dessau, Berlin, Chicago (MIT, Cambridge, MA, 1969).
6. D.A. Huffman, IEEE Trans. Comput. C-25, 1010 (1976). ITCOB4 0018-9340 10.1109/TC.1976.1674542
7. J.P. Duncan and J.L. Duncan, Proc. R. Soc. A 383, 191 (1982). PRLAAZ 1364-5021 10.1098/rspa.1982.0126
8. D. Fuchs and S. Tabachnikov, Am. Math. Mon. 106, 27 (1999). AMMYAE 0002-9890 10.2307/2589583
9. H. Pottmann and J. Wallner, Computational Line Geometry (Springer-Verlag, Berlin, 2001).
10. M. Kilian, S. Flöry, Z. Chen, N.J. Mitra, A. Sheffer, and H. Pottmann, ACM Trans. Graph. 27, 1 (2008). ATGRDF 0730-0301 10.1145/1360612. 1360674
11. J.P. Duncan, J.L. Duncan, R. Sowerby, and B.S. Levy, Sheet Metal Industries 58, 527 (1981). SHMIAR
12. K.A. Seffen, Phil. Trans. R. Soc. A 370, 2010 (2012). PTRMAD 1364-503X 10.1098/rsta.2011.0347
13. E.L. Starostin and G.H.M. van der Heijden, Phys. Rev. E 79, 066602 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.79.066602
14. B. Audoly and Y. Pomeau, Elasticity and Geometry: From Hair Curls to the Nonlinear Response of Shells (Oxford University, New York, 2010).
15. C.D. Santangelo, Europhys. Lett. 86, 34003 (2009). EULEEJ 0295-5075 10.1209/0295-5075/86/34003
16. M.P. do Carmo, Differential Geometry of Curves and Surfaces (Prentice-Hall, Englewood Cliffs, NJ, 1976).
17. A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity (Dover, New York, 1944).
18. R. Bridson, S. Marino, and R. Fedkiw, ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA), 2003, pp. 28-32.
19. See Supplemental Material at http://link.aps.org/supplemental/10.1103/ PhysRevLett.109.114301 for a derivation of the fold energy and analytical perturbation theory.
20. R. Capovilla, C. Chryssomalakos, and J. Guven, J. Phys. A 35, 6571 (2002). JPHAC5 0305-4470 10.1088/0305-4470/35/31/304
21. V.D. Sedykh, Bull. Lond. Math. Soc. 26, 177 (1994). LMSBBT 0024-6093 10.1112/blms/26.2.177