Advertisement

Abrupt out-of-plane edge folding of a circular thin plate: Implication for a mature Victoria regia leaf

  • Pengfei Yang
  • Chen Zhang
  • Fei Dang
  • Yuan Yan
  • Yilun Liu
  • Xi Chen
Regular Article

Abstract.

Inspired by the observation of the configurations of Victoria regia leaves, we establish a phenomenological buckling model for the abrupt out-of-plane edge folding of a circular thin sheet. A reduced model is first developed, and further refined by a more sophisticated growth strain field so that the resulting buckling morphology resembles that of a mature Victoria regia leaf. Parametric studies are carried out to investigate the effects of geometric, material, and strain field parameters on the buckling morphology. Several main characteristics discovered through numerical studies are verified by theoretical analysis of a simple geometry-based model. Besides, the roles of the thickness variation and cracks are examined. This work may not only shed some light on the morphogenesis of certain plants, but also provide some useful insights on three-dimensional fabrications using mechanical self-assembly.

Graphical abstract

Keywords

Soft Matter: Self-organisation and Supramolecular Assemblies 

References

  1. 1.
    P.B. Green, C.S. Steele, S.C. Rennich, Ann. Bot. 77, 515 (1996)CrossRefGoogle Scholar
  2. 2.
    P.B. Green, Am. J. Bot. 86, 1059 (1999)CrossRefGoogle Scholar
  3. 3.
    P.D. Shipman, A.C. Newell, Phys. Rev. Lett. 92, 4671 (2004)CrossRefGoogle Scholar
  4. 4.
    E. Sharon, M. Marder, H.L. Swinney, Am. Sci. 92, 254 (2004)CrossRefGoogle Scholar
  5. 5.
    E. Sharon, B. Roman, H.L. Swinney, Phys. Rev. E 75, 77 (2007)CrossRefGoogle Scholar
  6. 6.
    H. Xiao, X. Chen, Soft Matter 7, 10794 (2011)ADSCrossRefGoogle Scholar
  7. 7.
    J. Yin, X. Chen, I. Sheinman, J. Mech. Phys. Solids 57, 1470 (2009)ADSCrossRefGoogle Scholar
  8. 8.
    J. Wu, X. Chen, J. Phys. D 46, 1 (2013)Google Scholar
  9. 9.
    U. Nath, B.C.W. Crawford, R. Carpenter, E. Coen, Science 299, 1404 (2003)CrossRefGoogle Scholar
  10. 10.
    A.J. Fleming, S. McQueen-Mason, T. Mandel, C. Kuhlemeier, Science 276, 1415 (1997)CrossRefGoogle Scholar
  11. 11.
    Y. Klein, E. Efrati, E. Sharon, Science 315, 1116 (2007)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    E. Sharon, E. Efrati, Soft Matter 6, 5693 (2010)ADSCrossRefGoogle Scholar
  13. 13.
    D. Nielsen, Design Nature (WIT, Southampton, 2010)Google Scholar
  14. 14.
    L. Jin, S. Cai, Z. Suo, EPL 95, 64002 (2011)ADSCrossRefGoogle Scholar
  15. 15.
    J.Y. Sun, S. Xia, M.W. Moon, K.H. Oh, K.S. Kim, Proc. Royal Soc. London Ser. A 468, 932 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    F.S. Jeng, K.P. Huang, J. Struct. Geol. 30, 633 (2008)ADSCrossRefGoogle Scholar
  17. 17.
    S. Gyasi, R.B. Fridley, P. Chen, ASABE 24, 747 (1981)Google Scholar
  18. 18.
    C. Wei, P.M. Lintilhac, Plant Physiol. 145, 763 (2007)CrossRefGoogle Scholar
  19. 19.
    L.J. Gibson, M.F. Ashby, K.E. Easterling, J. Mater. Sci. 23, 3041 (1988)ADSCrossRefGoogle Scholar
  20. 20.
    J.H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics (Trafford, Victoria, 2001)Google Scholar
  21. 21.
    D.J. Beebe, J.S. Moore, J.M. Bauer, Q. Yu, R.H. Liu, C. Devadoss, B.H. Jo, Nature 404, 588 (2000)ADSCrossRefGoogle Scholar
  22. 22.
    T. Miyata, N. Asami, T. Uragami, Nature 399, 766 (1999)ADSCrossRefGoogle Scholar
  23. 23.
    W.R. Drummond, M.L. Knight, M.L. Brannon, N.A. Peppas, J. Controlled Release 7, 181 (1988)CrossRefGoogle Scholar
  24. 24.
    M. Abendroth, M. Kuna, Comput. Mater. Sci. 28, 633 (2003)CrossRefGoogle Scholar
  25. 25.
    R. Khalifehzadeha, S. Forouzanb, H. Aramib, S.K. Sadrnezhaad, Comput. Mater. Sci. 40, 359 (2007)CrossRefGoogle Scholar
  26. 26.
    A. Paradis, P. Terriault, V. Brailovski, Comput. Mater. Sci. 47, 373 (2009)CrossRefGoogle Scholar
  27. 27.
    S. Yang, K. Krishnacharya, P. Lin, Adv. Funct. Mater. 20, 2550 (2010)CrossRefGoogle Scholar
  28. 28.
    J. Yin, X. Chen, J. Phys. D 43, 115402 (2010)ADSCrossRefGoogle Scholar
  29. 29.
    X. Chen, J. Yin, Soft Matter 6, 5667 (2010)ADSCrossRefGoogle Scholar
  30. 30.
    A. Schweikart, A. Fery, Microchim. Acta 165, 75 (2009)CrossRefGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Pengfei Yang
    • 1
  • Chen Zhang
    • 1
  • Fei Dang
    • 1
  • Yuan Yan
    • 1
  • Yilun Liu
    • 2
  • Xi Chen
    • 3
  1. 1.International Center for Applied Mechanics, State Key Laboratory for Strength and Vibration of Mechanical Structures, School of AerospaceXi’an Jiaotong UniversityXi’anChina
  2. 2.State Key Laboratory for Strength and Vibration of Mechanical Structures, School of AerospaceXi’an Jiaotong UniversityXi’anChina
  3. 3.Columbia Nanomechanics Research Center, Department of Earth and Environmental EngineeringColumbia UniversityNew YorkUSA

Personalised recommendations