From flat sheets to curved geometries: Origami and kirigami approaches

Materials Today

Volumn 21, Issue 3, 2018, Pages 241-264

  Callens, Sebastien J P ^a   Zadpoor, Amir A ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

[No Author keywords available]

Indexed keywords

SURFACE TOPOGRAPHY;

ADVANCED MATERIALS; COMPLEX GEOMETRIES; FLAT STRUCTURES; FUTURE APPLICATIONS; INTRINSIC CURVATURE; MANUFACTURING PARADIGM; THREE DIMENSIONAL GEOMETRY; THREE-DIMENSIONAL STRUCTURE;

GEOMETRY;

EID: 85034455612     PISSN: 13697021     EISSN: 18734103     Source Type: Journal    
DOI: 10.1016/j.mattod.2017.10.004     Document Type: Review

References (174)

1. Zadpoor, A.A., Malda, J., Ann. Biomed. Eng. 45:1 (2017), 1–11.
2. Kadic, M., et al. Appl. Phys. Lett., 100(19), 2012, 191901.
3. Hedayati, R., Leeflang, A.M., Zadpoor, A.A., Appl. Phys. Lett., 110(9), 2017, 091905.
4. Bobbert, F.S.L., et al. Acta Biomater. 53 (2017), 572–584.
5. Duoss, E.B., et al. Adv. Funct. Mater. 24:31 (2014), 4905–4913.
6. Jiang, T., Guo, Z., Liu, W., J. Mater. Chem. A 3:5 (2015), 1811–1827.
7. Loh, O.Y., Espinosa, H.D., Nat. Nanotech. 7:5 (2012), 283–295.
8. Dobbenga, S., Fratila-Apachitei, L.E., Zadpoor, A.A., Acta Biomater. 46 (2016), 3–14.
9. Felton, S.M., et al. Soft Matter 9:32 (2013), 7688–7694.
10. Santangelo, C.D., Annu. Rev. Conden. Map., 8(1), 2016.
11. Liu, Y., Genzer, J., Dickey, M.D., Prog. Polym. Sci. 52 (2016), 79–106.
12. Guseinov, R., Miguel, E., Bickel, B., ACM Trans. Graph. 36:4 (2017), 1–12.
13. Hubbard, A.M., et al. Soft Matter 13:12 (2017), 2299–2308.
14. Rogers, J., et al. MRS Bull. 41:02 (2016), 123–129.
15. Bassik, N., Stern, G.M., Gracias, D.H., Appl. Phys. Lett., 95(9), 2009, 91901.
16. Leong, T.G., Zarafshar, A.M., Gracias, D.H., Small 6:7 (2010), 792–806.
17. Li, M.Z., et al. J. Mater. Process. Technol. 129 (2002), 333–338.
18. Gutowski, T., et al. Compos. Manuf. 2 (1991), 147–152.
19. Klein, Y., Efrati, E., Sharon, E., Science 315:5815 (2007), 1116–1120.
20. Gladman, A.S., et al. Nat. Mater. 15:4 (2016), 413–418.
21. Kim, J., et al. Science 335:6073 (2012), 1201–1205.
22. Sharon, E., Marder, M., Swinney, H.L., Am. Sci. 92 (2004), 254–261.
23. Sharon, E., et al. Nature, 419, 2002, 579.
24. Liang, H., Mahadevan, L., Proc. Natl. Acad. Sci. USA 108:14 (2011), 5516–5521.
25. Miura, K., Inst. Space Astronaut. Sci. Rep. 618 (1985), 1–9.
26. Guest, S.D., Pellegrino, S., Inextensional wrapping of flat membranes, in: Motro, R., Wester, T. (eds.), First Int. Sem. on Struct. Morph., Montpellier, 1992, pp 203–215.
27. Zirbel, S.A., et al. J. Mech. Des., 135(11), 2013, 111005.
28. Schenk, M., Guest, S.D., Proc. Natl. Acad. Sci. USA 110:9 (2013), 3276–3281.
29. Filipov, E.T., Tachi, T., Paulino, G.H., Proc. Natl. Acad. Sci. USA 112:40 (2015), 12321–12326.
30. Silverberg, J.L., et al. Science 345:6197 (2014), 647–650.
31. Overvelde, J.T., et al. Nature 541:7637 (2017), 347–352.
32. Eidini, M., Paulino, G.H., Sci. Adv., 1, 2015, 8.
33. Felton, S., et al. Science 345:6197 (2014), 644–646.
34. Kuribayashi, K., et al. Mater. Sci. Eng. A 419:1–2 (2006), 131–137.
35. Randall, C.L., et al. Adv. Drug. Deliv. Rev. 59:15 (2007), 1547–1561.
36. Randall, C.L., Gultepe, E., Gracias, D.H., Trends Biotechnol. 30:3 (2012), 138–146.
37. Lang, R.J., Phys. World, 20(2), 2007, 30.
38. Song, Z., et al. Sci. Rep., 5, 2015, 10988.
39. Shyu, T.C., et al. Nat. Mater. 14:8 (2015), 785–789.
40. Cho, Y., et al. Proc. Natl. Acad. Sci. USA 111:49 (2014), 17390–17395.
41. Hyde, S., et al. The Language of Shape: The Role of Curvature in Condensed Matter: Physics, Chemistry and Biology. 1996, Elsevier Science, Amsterdam, The Netherlands.
42. Hilbert, D., Cohn-Vossen, S., Geometry and The Imagination. 1990, Chelsea Publishing Company, New York, USA.
43. Weeks, J.R., The Shape of Space. 2001, CRC Press, Boca Raton, FL, USA.
44. Calladine, C.R., Theory of Shell Structures. 1983, Cambridge University Press, Cambridge, UK.
45. Toponogov, V.A., Rovenski, V., Differential Geometry of Curves and Surfaces: A Concise Guide. 2005, Birkhäuser Boston, New York, NY, USA.
46. Rovenski, V., Modeling of Curves and Surfaces with MATLAB. 2010, Springer Science & Business Media, New York, NY, USA.
47. Spivak, M., A Comprehensive Introduction to Differential Geometry, vol. II, 1990, Publish or Perish, Inc., Houston, Texas, USA.
48. O‘Neill, B., Elementary Differential Geometry. 2006, Academic Press (Elsevier), Burlington, MA, USA.
49. Sharon, E., Efrati, E., Soft Matter, 6(22), 2010, 5693.
50. Marder, M., Deegan, R.D., Sharon, E., Phys. Today 60:2 (2007), 33–38.
51. Kamien, R.D., Science 315 (2007), 1083–1084.
52. Pressley, A.N., Elementary Differential Geometry. 2010, Springer Science & Business Media, Dordrecht, The Netherlands.
53. Efrati, E., et al. Phys. D 235:1–2 (2007), 29–32.
54. Aharoni, H., Sharon, E., Kupferman, R., Phys. Rev. Lett., 113(25), 2014, 257801.
55. Witten, T.A., Rev. Mod. Phys. 79:2 (2007), 643–675.
56. Efrati, E., Sharon, E., Kupferman, R., J. Mech. Phys. Solids 57:4 (2009), 762–775.
57. Demaine, E., Demaine, M., Recent results in computational origami. Hull, T., (eds.) Origami 3: Proceedings of the 3rd International Meeting of Origami Science, Math, and Education (OSME 2001), 2002, A K Peters/CRC Press, Boca Raton, FL, USA, 3–16.
58. Demaine, E.D., Demaine, M.L., Mitchell, J.S.B., Comput. Geom. 16:1 (2000), 3–21.
59. Tachi, T., IEEE Trans. Vis. Comput. Graphics 16:2 (2010), 298–311.
60. Abel, Z., et al. J. Comput. Geom. 7 (2016), 171–184.
61. Evans, T.A., et al. R. Soc. Open Sci., 2(9), 2015, 150067.
62. Castle, T., et al. Phys. Rev. Lett., 113(24), 2014, 245502.
63. Miura, K., A note on intrinsic geometry of origami, in: Huzita, H., (ed.), First Int. Meeting of Origami Science and Technology, Ferrara, Italy, 1989, pp 239–249.
64. Huffman, D.A., IEEE Trans. Comput. C-25:10 (1976), 1010–1019.
65. Hull, T., Project origami: activities for exploring mathematics. second ed., 2012, CRC Press, Boca Raton, FL, USA.
66. Alperin, R.C., Hayes, B., Lang, R.J., Math. Intell. 34:2 (2012), 38–49.
67. Gjerde, E., Origami Tessellations Awe-Inspiring Geometric Designs. 2008, A K Peters/CRC Press, Boca Raton, FL, USA.
68. Seffen, K.A., Philos. Trans. A Math. Phys. Eng. Sci. 370:1965 (2012), 2010–2026.
69. Evans, A.A., Silverberg, J.L., Santangelo, C.D., Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 92(1), 2015, 013205.
70. Mahadevan, L., Rica, S., Science, 307, 2005.
71. Lv, C., et al. Sci. Rep., 4, 2014, 5979.
72. Schenk, M., Guest, S.D., Origami folding: A structural engineering approach. Wang-Iverson, P., et al. (eds.) Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME), 2011, A K Peters/CRC Press, Boca Raton, FL, 291–304.
73. Tachi, T., J. Int. Assoc. Shell Spatial Struct. 50:3 (2009), 173–179.
74. Gattas, J.M., Wu, W., You, Z., J. Mech. Des. 135:11 (2013), 1110111–11101111.
75. Sareh, P., Guest, S.D., Int. J. Space Struct. 30:2 (2015), 141–152.
76. Wang, F., Gong, H., Chen, X., Chen, C.Q., Sci. Rep., 6, 2016, 33312.
77. Dudte, L.H., Vouga, E., Tachi, T., Mahadevan, L., Nat. Mater. 15:5 (2016), 583–588.
78. Chen, Y., et al. Proc. R. Soc. A, 472(2190), 2016, 20150846.
79. Resch, R.D., The Topological Design of Sculptural and Architectural Systems. 1973, Nat. Comp. Conf. and Exp., ACM, New York, 643–650.
80. Resch, R.D., Christiansen, H., The design and analysis of kinematic folded plate systems, in: IASS Symp. on Folded Plates and Prism. Struct., Vienna, 1970.
81. Tachi, T., J. Mech. Des., 135, 2013, 111006.
82. Tachi, T., Rigid folding of periodic origami tessellations. Miura, K., et al. (eds.) Origami 6: Mathematics, 2016, American Mathematical Society, Providence, RI, USA.
83. Nassar, H., Lebee, A., Monasse, L., Proc. R. Soc. A, 473(2197), 2017, 20160705.
84. Tachi, T., J. Geom. Graph. 14:2 (2010), 203–215.
85. Zhou, X., Wang, H., You, Z., Proc. R. Soc. A, 471(2181), 2015, 20150407.
86. Song, K., et al. Proc. R. Soc. A, 473(2200), 2017, 20170016.
87. Lang, R.J., A computational algorithm for origami design, in: Twelfth Ann. Symp. on Comput. Geom., Philadelphia, 1996.
88. Tachi, T., 3D origami design based on tucking molecules, in: Lang, R. J., (ed.), Origami 4, Proceedings of 4OSME: 4th International Conference on Origami in Science, Mathematics and Education, A K Peters/CRC Press, Boca Raton, Fl, USA, 2009, pp 259–272.
89. Demaine, E., Tachi, T., Origamizer: a practical algorithm for folding any polyhedron, in: Aronov, B., and Katz, M. J., (eds.), 33rd Int. Symp. on Comput. Geom. (SoCG 2017), Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, Germany, 2017.
90. Demaine, E.D., et al. Symm. Cult. Sci. 26:2 (2015), 145–161.
91. Duncan, J.P., Duncan, J.L., Proc. R. Soc. A 383:1784 (1982), 191–205.
92. Geretschläger, R., Folding curves, in: Lang, R. J., (ed.), Origami 4, Proceedings of 4OSME: 4th International Conference on Origami in Science, Mathematics and Education, A K Peters/CRC Press, Boca Raton, FL, USA, (2009), pp 151–163.
93. Kilian, M., Monszpart, A., Mitra, N.J., ACM Trans. Graph. 36:3 (2017), 1–13.
94. Fuchs, D., Tabachnikov, S., Am. Math. Month. 106 (1999), 27–35.
95. Kilian, M., et al. ACM Trans. Graph., 27, 2008, 75.
96. Vergauwen, A., Laet, L.D., Temmerman, N.D., Comput. Aided Des. 83 (2017), 51–63.
97. Leong, C. C., Simulation of nonzero gaussian curvature in origami by curved crease couplets, in: Lang, R. J., (ed.), Origami 4, Proceedings of 4OSME: 4th International Conference on Origami in Science, Mathematics and Education, A.K. Peters/CRC Press, Boca Raton, FL, USA, 2009, pp 151–163.
98. Mitani, J., Comput. Aided Des. Appl. 6:1 (2009), 69–79.
99. Lang, R. J., Origami Flanged Pots, http://demonstrations.wolfram.com/OrigamiFlangedPots/, in: Wolfram Demonstrations Project, vol. 2017.
100. Lang, R.J., Origami Design Secrets: Mathematical Methods for an Ancient Art. second ed., 2011, A K Peters/CRC Press, Boca Raton, FL, USA.
101. Mitani, J., A design method for axisymmetric curved origami with triangular prism protrusions. Wang-Iverson, P., et al. (eds.) Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME), 2011, A K Peters/CRC Press, Boca Raton, FL, 437–447.
102. Demaine, E.D., et al. Characterization of curved creases and rulings design and analysis of lens tessellations. Miura, K., et al. (eds.) Origami 6: Mathematics, 2016, American Mathematical Society, Providence, RI, USA, 209–230.
103. Bende, N.P., et al. Proc. Natl. Acad. Sci. USA 112:36 (2015), 11175–11180.
104. Demaine, E.D., Demaine, M.L., Hart, V., Price, G.N., Tachi, T., Graphs Combin. 27:3 (2011), 377–397.
105. van Manen, T., Janbaz, S., Zadpoor, A.A., Mater. Horiz., 2017, 10.1039/C7MH00269F.
106. Schenk, M., Folded Shell Structures. (Ph.D. thesis), 2011, University of Cambridge.
107. Tachi, T., Simulation of rigid origami, in: Lang, R. J., (ed.), Origami 4, Proceedings of 4OSME: 4th International Conference on Origami in Science, Mathematics and Education, A K Peters/CRC Press, Boca Raton, FL, USA, 2009.
108. Wei, Z.Y., et al. Phys. Rev. Lett., 110(21), 2013, 215501.
109. Mouthuy, P.O., et al. Nat. Commun., 3, 2012, 1290.
110. Dias, M.A., et al. Phys. Rev. Lett., 109(11), 2012, 114301.
111. Dias, M.A., Santangelo, C.D., EPL (Europhys. Lett.), 100(5), 2012, 54005.
112. Demaine, E. D., Demaine, M. L., Lubiw, A., Polyhedral sculptures with hyperbolic paraboloids, in: 2nd Ann. Conf. of BRIDGES: Mathematical Connections in Art, Music, and Science, Kansas, USA, 1999.
113. Blees, M.K., et al. Nature 524:7564 (2015), 204–207.
114. Lamoureux, A., et al. Nat. Commun., 6, 2015, 8092.
115. Neville, R.M., Scarpa, F., Pirrera, A., Sci. Rep., 6, 2016, 31067.
116. Saito, K., Agnese, F., Scarpa, F., J. Intell. Mater. Syst. Struct. 22:9 (2011), 935–944.
117. Del Broccolo, S., Laurenzi, S., Scarpa, F., Compos. Struct. 176 (2017), 433–441.
118. Irvine, W.T., Vitelli, V., Chaikin, P.M., Nature 468:7326 (2010), 947–951.
119. Sadoc, J.F., Rivier, N., Charvolin, J., Acta Crystallogr. Sect. A: Found. Crystallogr. 68:4 (2012), 470–483.
120. Martin, A.G., A basketmaker's approach to structural morphology, in: Int. Assoc. Shell Spatial Struct. (IASS) Symp., Amsterdam, The Netherlands, 2015.
121. Charvolin, J., Sadoc, J.-F., Biophys. Rev. Lett. 06:01n02 (2011), 13–27.
122. Sussman, D.M., et al. Proc. Natl. Acad. Sci. USA 112:24 (2015), 7449–7453.
123. Castle, T., et al. Sci. Adv., 2(9), 2016, e1601258.
124. Wang, F., et al. J. Appl. Mech., 84(6), 2017, 061007.
125. Tang, Y., et al. Adv. Mater., 29(10), 2016, 1604262.
126. Rafsanjani, A., Bertoldi, K., Phys. Rev. Lett., 118(8), 2017, 084301.
127. Yang, S., Choi, I.-S., Kamien, R.D., MRS Bull. 41:02 (2016), 130–138.
128. Tang, Y., et al. Adv. Mater. 27:44 (2015), 7181–7190.
129. Tang, Y., Yin, J., Extr. Mech. Lett. 12 (2017), 77–85.
130. Gatt, R., et al. Sci. Rep., 5, 2015, 8395.
131. Kolken, H.M.A., Zadpoor, A.A., RSC Adv. 7:9 (2017), 5111–5129.
132. Ben Amar, M., Pomeau, Y., Proc. R. Soc. A 453:1959 (1997), 729–755.
133. Peraza-Hernandez, E.A., et al. Smart Mater. Struct., 23(9), 2014, 094001.
134. Hawkes, E., et al. Proc. Natl. Acad. Sci. USA 107:28 (2010), 12441–12445.
135. Janbaz, S., Hedayati, R., Zadpoor, A.A., Mater. Horiz. 3:6 (2016), 536–547.
136. Kuribayashi-Shigetomi, K., Onoe, H., Takeuchi, S., PLoS One, 7(12), 2012, e51085.
137. Tolley, M.T., et al. Smart Mater. Struct., 23(9), 2014, 094006.
138. Liu, Y., et al. Soft Matter 8:6 (2012), 1764–1769.
139. Davis, D., et al. RSC Adv. 5:108 (2015), 89254–89261.
140. Davis, D., et al. J. Mech. Robot., 8(3), 2016, 031014.
141. Guan, J., et al. J. Phys. Chem. B 109:49 (2005), 23134–23137.
142. Stoychev, G., Puretskiy, N., Ionov, L., Soft Matter 7:7 (2011), 3277–3279.
143. Gimi, B., et al. Biomed. Microdevices 7:4 (2005), 341–345.
144. Azam, A., et al. Biomed. Microdevices 13:1 (2011), 51–58.
145. Gracias, D.H., et al. Adv. Mater., 14(3), 2002, 235.
146. Yan, Z., et al. Adv. Funct. Mater. 26:16 (2016), 2629–2639.
147. Zhang, Y., et al. Proc. Natl. Acad. Sci. USA 112:38 (2015), 11757–11764.
148. Zhang, Y., et al. Nat. Rev. Mater., 2(4), 2017, 17019.
149. Van Manen, T., Janbaz, S., Zadpoor, A.A., Mater. Today 21:2 (2018), 144–163.
150. Tachi, T., Hull, T.C., J. Mech. Robot., 9(2), 2017 021008-021008-021009.
151. Liu, Y., Shaw, B., Dickey, M.D., Genzer, J., Sci. Adv., 3, 2017, 3.
152. Na, J.H., et al. Adv. Mater. 27:1 (2015), 79–85.
153. Zhang, Q., et al. Extr. Mech. Lett. 11 (2017), 111–120.
154. Shi, Y., et al. Extr. Mech. Lett. 11 (2017), 105–110.
155. Ahn, B.Y., Shoji, D., Hansen, C.J., et al. Adv. Mater. 22:20 (2010), 2251–2254.
156. Mao, Y., et al. Sci. Rep., 5, 2015, 13616.
157. Lauff, C., et al., Differentiating bending from folding in origami engineering using active materials, in: Proceedings of the ASME 2014 International Design Engineering Technical Conferences & Computers and Information Engineering Conference, 2014, p V05BT08A040.
158. Chen, Y., Peng, R., You, Z., Science 349:6246 (2015), 396–400.
159. Tachi, T., Rigid-foldable thick origami. Wang-Iverson, P., et al. (eds.) Origami 5: Fifth International Meeting of Origami Science, Mathematics, and Education (5OSME), 2011, A K Peters/CRC Press, Boca Raton, FL, 253–263.
160. Lang, R.J., et al. J. Mech. Robot., 9(2), 2017, 021013.
161. Peraza Hernandez, E.A., Hartl, D.J., Lagoudas, D.C., Proc. R. Soc. A, 473(2200), 2017, 20160716.
162. An, N., Li, M., Zhou, J., Smart Mater. Struct., 25(11), 2016, 11LT02.
163. Xu, L., Shyu, T.C., Kotov, N.A., ACS Nano 11 (2017), 7587–7599.
164. Silverberg, J.L., Na, J.H., Evans, A.A., et al. Nat. Mater. 14:4 (2015), 389–393.
165. Leong, T.G., et al. Proc. Natl. Acad. Sci. USA 106:3 (2009), 703–708.
166. Jamal, M., et al. Biomaterials 31:7 (2010), 1683–1690.
167. Zadpoor, A.A., Biomater. Sci. 3:2 (2015), 231–245.
168. Kapfer, S.C., et al. Biomaterials 32:29 (2011), 6875–6882.
169. Blanquer, S.B., et al. Biofabrication, 9(2), 2017, 025001.
170. Michielsen, K., Stavenga, D.G., J. R. Soc. Interface 5:18 (2008), 85–94.
171. Galusha, J.W., et al. Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 77(5 Pt. 1), 2008, 050904.
172. Jinnai, H., et al. Adv. Mater. 14:22 (2002), 1615–1618.
173. Evans, M.E., Schröder-Turk, G.E., Asia Pacific Math. Newslett. 5:2 (2015), 21–30.
174. Hyde, S.T., Schröder-Turk, G.E., Interface Focus 2 (2012), 529–538.