1932

Abstract

Many objects in nature and industry are wrapped in a thin sheet to enhance their chemical, mechanical, or optical properties. Similarly, there are a variety of methods for wrapping, from pressing a film onto a hard substrate to inflating a closed membrane, to spontaneously wrapping droplets using capillary forces. Each of these settings raises challenging nonlinear problems involving the geometry and mechanics of a thin sheet, often in the context of resolving a geometric incompatibility between two surfaces. Here, we review recent progress in this area, focusing on highly bendable films that are nonetheless hard to stretch, a class of materials that includes polymer films, metal foils, textiles, and graphene, as well as some biological materials. Significant attention is paid to two recent advances: a novel isometry that arises in the doubly-asymptotic limit of high flexibility and weak tensile forcing, and a simple geometric model for predicting the overall shape of an interfacial film while ignoring small-scale wrinkles, crumples, and folds.

Loading

Article metrics loading...

/content/journals/10.1146/annurev-conmatphys-031218-013533
2019-03-10
2024-10-14
Loading full text...

Full text loading...

/deliver/fulltext/conmatphys/10/1/annurev-conmatphys-031218-013533.html?itemId=/content/journals/10.1146/annurev-conmatphys-031218-013533&mimeType=html&fmt=ahah

Literature Cited

  1. 1.  Demaine ED, Demaine ML, Iacono J, Langerman S 2009. Comput. Geom. 42:748–57
    [Google Scholar]
  2. 2.  Chen Y, Guo F, Jachak A, Kim SP, Datta D et al. 2012. Nano Lett. 12:1996–2002
    [Google Scholar]
  3. 3.  Py C, Reverdy P, Doppler L, Bico J, Roman B, Baroud C 2007. Phys. Fluids 19:091104
    [Google Scholar]
  4. 4.  Audoly B, Pomeau Y 2010. Elasticity and Geometry: From Hair Curls to the Non-Linear Response of Shells New York: Oxford Univ. Press
    [Google Scholar]
  5. 5.  Vishtal A, Retulainen E 2014. BioResources 9:7951–8001
    [Google Scholar]
  6. 6.  Landau LD, Lifshitz E 1986. Theory of Elasticity 7 Course of Theoretical Physics New York: Elsevier, 3rd ed
    [Google Scholar]
  7. 7.  Feynman RP, Leighton RB, Sands M 1964. The Feynman Lectures on Physics 2 Mainly Electromagnetism and Matter New York: Addison-Wesley
    [Google Scholar]
  8. 8.  Bowden N, Brittain S, Evans AG, Hutchinson JW, Whitesides GM 1998. Nature 393:146–49
    [Google Scholar]
  9. 9.  Brau F, Vandeparre H, Sabbah A, Poulard C, Boudaoud A, Damman P 2011. Nat. Phys. 7:56–60
    [Google Scholar]
  10. 10.  Pocivavsek L, Dellsy R, Kern A, Johnson S, Lin B et al. 2008. Science 320:912–16
    [Google Scholar]
  11. 11.  Diamant H, Witten TA 2011. Phys. Rev. Lett. 107:164302
    [Google Scholar]
  12. 12.  Brau F, Damman P, Diamant H, Witten TA 2013. Soft Matter 9:8177–86
    [Google Scholar]
  13. 13.  Davidovitch B, Schroll RD, Cerda E 2012. Phys. Rev. E 85:066115
    [Google Scholar]
  14. 14.  Huang J, Davidovitch B, Santangelo CD, Russell TP, Menon N 2010. Phys. Rev. Lett. 105:038302
    [Google Scholar]
  15. 15.  Cerda E, Mahadevan L 2003. Phys. Rev. Lett. 90:074302
    [Google Scholar]
  16. 16.  Paulsen JD, Hohlfeld E, King H, Huang J, Qiu Z et al. 2016. PNAS 113:1144–49
    [Google Scholar]
  17. 17.  Taffetani M, Vella D 2017. Philos. Trans. R. Soc. A 375:20160330
    [Google Scholar]
  18. 18.  Huang J, Juszkiewicz M, de Jeu WH, Cerda E, Emrick T et al. 2007. Science 317:650–53
    [Google Scholar]
  19. 19.  Chung JY, Nolte AJ, Stafford CM 2011. Adv. Mater. 23:349–68
    [Google Scholar]
  20. 20.  Efimenko K, Rackaitis M, Manias E, Vaziri A, Mahadevan L, Genzer J 2005. Nat. Mater. 4:293–97
    [Google Scholar]
  21. 21.  Chung JY, Youngblood JP, Stafford CM 2007. Soft Matter 3:1163–69
    [Google Scholar]
  22. 22.  Chan EP, Smith EJ, Hayward RC, Crosby AJ 2008. Adv. Mater. 20:711–16
    [Google Scholar]
  23. 23.  Zang J, Ryu S, Pugno N, Wang Q, Tu Q et al. 2013. Nat. Mater. 12:321–25
    [Google Scholar]
  24. 24.  Levien R 2008. The elastica: a mathematical history. Tech. Rep. UCB/EECS-2008-103, Univ. Calif., Berkeley
  25. 25.  Giomi L, Mahadevan L 2012. Proc. R. Soc. A 468:1851–64
    [Google Scholar]
  26. 26.  Romero V, Witten T, Cerda E 2008. Philos. Trans. R. Soc. Lond. A 464:2847–66
    [Google Scholar]
  27. 27.  Audoly B 2011. Phys. Rev. E 84:011605
    [Google Scholar]
  28. 28.  Démery V, Davidovitch B, Santangelo CD 2014. Phys. Rev. E 90:042401
    [Google Scholar]
  29. 29.  Oshri O, Brau F, Diamant H 2015. Phys. Rev. E 91:052408
    [Google Scholar]
  30. 30.  Py C, Reverdy P, Doppler L, Bico J, Roman B, Baroud CN 2007. Phys. Rev. Lett. 98:156103
    [Google Scholar]
  31. 31.  Sharon E, Roman B, Marder M, Shin G-S, Swinney HL 2002. Nature 419:579
    [Google Scholar]
  32. 32.  Struik DJ 1950. Lectures on Classical Differential Geometry Reading, MA: Addison-Wesley
    [Google Scholar]
  33. 33.  Bico J, Roman B, Moulin L, Boudaoud A 2004. Nature 432:690
    [Google Scholar]
  34. 34.  Paretkar D, Xu X, Hui CY, Jagota A 2014. Soft Matter 10:4084–90
    [Google Scholar]
  35. 35.  Mora S, Pomeau Y 2015. J. Phys. Condens. Matter 27:194112
    [Google Scholar]
  36. 36.  Style RW, Jagota A, Hui CY, Dufresne ER 2017. Annu. Rev. Condens. Matter Phys. 8:99–118
    [Google Scholar]
  37. 37.  Bico J, Reyssat É, Roman B 2017. Annu. Rev. Fluid Mech. 50:629–59
    [Google Scholar]
  38. 38.  Pokroy B, Kang SH, Mahadevan L, Aizenberg J 2009. Science 323:237–40
    [Google Scholar]
  39. 39.  Reis PM, Hure J, Jung S, Bush JWM, Clanet C 2010. Soft Matter 6:5705–8
    [Google Scholar]
  40. 40.  Skouras M, Thomaszewski B, Kaufmann P, Garg A, Bickel B et al. 2014. ACM Trans. Graph. 33:63
    [Google Scholar]
  41. 41.  Guo X, Li H, Yeop Ahn B, Duoss EB, Hsia KJ et al. 2009. PNAS 106:20149–54
    [Google Scholar]
  42. 42.  Jung S, Reis PM, James J, Clanet C, Bush JWM 2009. Phys. Fluids 21:091110
    [Google Scholar]
  43. 43.  Pogorelov AV 1973. Extrinsic Geometry of Convex Surfaces 35 Translations of Mathematical Monographs Providence: Am. Math. Soc
    [Google Scholar]
  44. [Google Scholar]
  45. 45.  Hong S, Asai T 2014. Sci. Rep. 4:5068
    [Google Scholar]
  46. 46.  Hure J, Roman B, Bico J 2012. Phys. Rev. Lett. 109:054302
    [Google Scholar]
  47. 47.  Hure J, Roman B, Bico J 2011. Phys. Rev. Lett. 106:174301
    [Google Scholar]
  48. 48.  Majidi C, Adams GG 2009. Philos. Trans. R. Soc. Lond. A 465:2217–30
    [Google Scholar]
  49. 49.  Hure J, Audoly B 2013. J. Mech. Phys. Solids 61:450–71
    [Google Scholar]
  50. 50.  Marchand A, Das S, Snoeijer JH, Andreotti B 2012. Phys. Rev. Lett. 108:094301
    [Google Scholar]
  51. 51.  Nadermann N, Hui CY, Jagota A 2013. PNAS 110:10541–45
    [Google Scholar]
  52. 52.  Schulman RD, Dalnoki-Veress K 2015. Phys. Rev. Lett. 115:206101
    [Google Scholar]
  53. 53.  Duprat C, Protiere S 2015. Europhys. Lett. 111:56006
    [Google Scholar]
  54. 54.  Grason GM, Davidovitch B 2013. PNAS 110:12893–98
    [Google Scholar]
  55. 55.  Roman B, Pocheau A 2012. Phys. Rev. Lett. 108:074301
    [Google Scholar]
  56. 56.  King H, Schroll RD, Davidovitch B, Menon N 2012. PNAS 109:9716–20
    [Google Scholar]
  57. 57.  Yao Z, Bowick M, Ma X, Sknepnek R 2013. Europhys. Lett. 101:44007
    [Google Scholar]
  58. 58.  Aharoni H, Todorova DV, Albarrán O, Goehring L, Kamien RD, Katifori E 2017. Nat. Commun. 8:15809
    [Google Scholar]
  59. 59.  Bella P, Kohn RV 2017. Philos. Trans. R. Soc. A 375:20160157
    [Google Scholar]
  60. 60.  Hohlfeld E, Davidovitch B 2015. Phys. Rev. E 91:012407
    [Google Scholar]
  61. 61.  Vella D, Huang J, Menon N, Russell TP, Davidovitch B 2015. Phys. Rev. Lett. 114:014301
    [Google Scholar]
  62. 62.  Chopin J, Démery V, Davidovitch B 2015. J. Elast. 119:137–89
    [Google Scholar]
  63. 63.  Vella D, Ebrahimi H, Vaziri A, Davidovitch B 2015. Europhys. Lett. 112:24007
    [Google Scholar]
  64. 64.  Lee C, Wei X, Kysar JW, Hone J 2008. Science 321:385–88
    [Google Scholar]
  65. 65.  Pharr GM, Herbert EG, Gao Y 2010. Annu. Rev. Mater. Res. 40:271–92
    [Google Scholar]
  66. 66.  Roos W, Bruinsma R, Wuite G 2010. Nat. Phys. 6:733
    [Google Scholar]
  67. 67.  Gordon VD, Chen X, Hutchinson JW, Bausch AR, Marquez M, Weitz DA 2004. J. Am. Chem. Soc. 126:14117–22
    [Google Scholar]
  68. 68.  Vella D, Ajdari A, Vaziri A, Boudaoud A 2012. Phys. Rev. Lett. 109:144302
    [Google Scholar]
  69. 69.  Lazarus A, Florijn H, Reis PM 2012. Phys. Rev. Lett. 109:144301
    [Google Scholar]
  70. 70.  Vella D, Ajdari A, Vaziri A, Boudaoud A 2011. Phys. Rev. Lett. 107:174301
    [Google Scholar]
  71. 71.  Vella D, Davidovitch B 2018. Phys. Rev. E 98:013003
    [Google Scholar]
  72. 72.  Holmes DP, Crosby AJ 2010. Phys. Rev. Lett. 105:038303
    [Google Scholar]
  73. 73.  Ripp MM, Démery V, Zhang T, Paulsen JD 2018. arXiv:1804.02421
  74. 74.  Gomez M, Moulton DE, Vella D 2016. Proc. R. Soc. A 472:20150732
    [Google Scholar]
  75. 75.  Vaziri A, Mahadevan L 2008. PNAS 105:7913–18
    [Google Scholar]
  76. 76.  Nasto A, Ajdari A, Lazarus A, Vaziri A, Reis PM 2013. Soft Matter 9:6796–803
    [Google Scholar]
  77. 77.  Green AE 1937. Philos. Trans. R. Soc. Lond. A 161:197–220
    [Google Scholar]
  78. 78.  Chopin J, Kudrolli A 2013. Phys. Rev. Lett. 111:174302
    [Google Scholar]
  79. 79.  Korte A, Starostin E, van der Heijden G 2011. Philos. Trans. R. Soc. Lond. A 467:285–303
    [Google Scholar]
  80. 80.  Dinh HP, Démery V, Davidovitch B, Brau F, Damman P 2016. Phys. Rev. Lett. 117:104301
    [Google Scholar]
  81. 81.  Audoly B, Boudaoud A 2003. Phys. Rev. Lett. 91:086105
    [Google Scholar]
  82. 82.  Giomi L, Mahadevan L 2010. Phys. Rev. Lett. 104:238104
    [Google Scholar]
  83. 83.  Klein Y, Venkataramani S, Sharon E 2011. Phys. Rev. Lett. 106:118303
    [Google Scholar]
  84. 84.  Gemmer J, Venkataramani S 2012. Nonlinearity 25:3553
    [Google Scholar]
  85. 85.  Dias MA, Dudte LH, Mahadevan L, Santangelo CD 2012. Phys. Rev. Lett. 109:114301
    [Google Scholar]
  86. 86.  Paulsen JD, Démery V, Santangelo CD, Russell TP, Davidovitch B, Menon N 2015. Nat. Mater. 14:1206–9
    [Google Scholar]
  87. 87.  Brakke KA 1992. Exp. Math. 1:141–65
    [Google Scholar]
  88. 88.  Gao L, McCarthy TJ 2008. Langmuir 24:9183–88
    [Google Scholar]
  89. 89.  Milner ST, Joanny JF, Pincus P 1989. Europhys. Lett. 9:495
    [Google Scholar]
  90. 90.  Hunt GW, Wadee MK, Shiacolas N 1993. J. Appl. Mech. 60:1033
    [Google Scholar]
  91. 91.  Reis PM, Corson F, Boudaoud A, Roman B 2009. Phys. Rev. Lett. 103:045501
    [Google Scholar]
  92. 92.  Leahy BD, Pocivavsek L, Meron M, Lam KL, Salas D et al. 2010. Phys. Rev. Lett. 105:058301
    [Google Scholar]
  93. 93.  Pineirua M, Tanaka N, Roman B, Bico J 2013. Soft Matter 9:10985–92
    [Google Scholar]
  94. 94.  Paulsen JD, Démery V, Toga KB, Qiu Z, Russell TP et al. 2017. Phys. Rev. Lett. 118:048004
    [Google Scholar]
  95. 95.  Kumar D, Paulsen JD, Russell TP, Menon N 2018. Science 359:775–78
    [Google Scholar]
  96. 96.  Binks BP 2002. Curr. Opin. Colloid Interface Sci. 7:21–41
    [Google Scholar]
  97. 97.  Subramaniam AB, Abkarian M, Mahadevan L, Stone HA 2005. Nature 438:930
    [Google Scholar]
  98. 98.  Cui M, Emrick T, Russell TP 2013. Science 342:460–63
    [Google Scholar]
  99. 99.  Paulsen WH 1994. Am. Math. Mon. 101:953–58
    [Google Scholar]
  100. 100.  Deakin MA 2009. B. Aust. Math. Soc. 80:506–9
    [Google Scholar]
  101. 101.  Salama M, Lou M, Fang H 2000. 41st Structures Struct. Dynam. Mater. Conf. Exhib. Atlanta, GA, Apr. 3–6 1730 Reston, VA: AIAA
    [Google Scholar]
  102. 102.  Mladenov IM, Oprea J 2009. J. Geom. Symmetry Phys. 15:53–88
    [Google Scholar]
  103. 103.  Pak I 2008. Am. Math. Mon. 115:443–45
    [Google Scholar]
  104. 104.  Bleecker DD 1996. J. Differ. Geom. 43:505–26
    [Google Scholar]
  105. 105.  Buchin K, Schulz A 2007. Proc. 23rd Annu. Symp. Comp. Geom. Gyeongju, South Korea, Jun. 6–8 125–126 New York, NY: ACM
    [Google Scholar]
  106. 106.  Alexandrov AD 2005. Convex Polyhedra New York: Springer
    [Google Scholar]
  107. 107.  Pak I 2006. Preprint, Department of Mathematics, MIT. http://math.ucla.edu/∼pak/papers/pillow4
    [Google Scholar]
  108. 108.  Taylor GI 1963. On the shapes of parachutes (paper written for the Advisory Committee for Aeronautics, 1919). 3 The Scientific Papers of Sir Geoffrey Ingram Taylor New York: Cambridge Univ. Press
    [Google Scholar]
  109. 109.  Pagitz M 2007. Philos. Trans. R. Soc. A 365:3003–17
    [Google Scholar]
  110. 110.  Lennon A, Pellegrino S 2005. Proc. Euro. Conf. Space. Struct. Mater. Mech. Testing K Fletcher Noordwijk, The Netherlands, May 10–12 101 Noordwijk, The Netherlands: ESA
    [Google Scholar]
  111. 111.  Pagitz M, Pellegrino S 2010. Int. J. Solids Struct. 47:1496–507
    [Google Scholar]
  112. 112.  Deng X, Pellegrino S 2011. 11th AIAA ATIO Conf. Virginia Beach, VA, Sep. 20–22 6830 Reston, VA: AIAA
    [Google Scholar]
  113. 113.  Barsotti R, Ligarò SS 2014. Comput. Mech. 53:1001–13
    [Google Scholar]
  114. 114.  Vetter R, Stoop N, Wittel FK, Herrmann HJ 2014. J. Phys. Conf. Ser. 487:012012
    [Google Scholar]
  115. 115.  Witten TA 2007. Rev. Mod. Phys. 79:643–75
    [Google Scholar]
  116. 116.  Blees MK, Barnard AW, Rose PA, Roberts SP, McGill KL et al. 2015. Nature 524:204
    [Google Scholar]
  117. 117.  Košmrlj A, Nelson DR 2016. Phys. Rev. B 93:125431
    [Google Scholar]
  118. 118.  Yllanes D, Bhabesh SS, Nelson DR, Bowick MJ 2017. Nat. Commun. 8:1381
    [Google Scholar]
  119. 119.  Shenoy VB, Gracias DH 2012. Mat. Res. Soc. Bull. 37:847–54
    [Google Scholar]
  120. 120.  Na JH, Evans AA, Bae J, Chiappelli MC, Santangelo CD et al. 2015. Adv. Mater. 27:79–85
    [Google Scholar]
  121. 121.  Xu W, Qin Z, Chen CT, Kwag HR, Ma Q et al. 2017. Sci. Adv. 3:e1701084
    [Google Scholar]
  122. 122.  Miskin MZ, Dorsey KJ, Bircan B, Han Y, Muller DA et al. 2018. PNAS 115:466–70
    [Google Scholar]
  123. 123.  Amstad E 2017. ACS Macro Lett. 6:841–47
    [Google Scholar]
/content/journals/10.1146/annurev-conmatphys-031218-013533
Loading
/content/journals/10.1146/annurev-conmatphys-031218-013533
Loading

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error