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.
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P.B. Green, C.S. Steele, S.C. Rennich, Ann. Bot. 77, 515 (1996)
P.B. Green, Am. J. Bot. 86, 1059 (1999)
P.D. Shipman, A.C. Newell, Phys. Rev. Lett. 92, 4671 (2004)
E. Sharon, M. Marder, H.L. Swinney, Am. Sci. 92, 254 (2004)
E. Sharon, B. Roman, H.L. Swinney, Phys. Rev. E 75, 77 (2007)
H. Xiao, X. Chen, Soft Matter 7, 10794 (2011)
J. Yin, X. Chen, I. Sheinman, J. Mech. Phys. Solids 57, 1470 (2009)
J. Wu, X. Chen, J. Phys. D 46, 1 (2013)
U. Nath, B.C.W. Crawford, R. Carpenter, E. Coen, Science 299, 1404 (2003)
A.J. Fleming, S. McQueen-Mason, T. Mandel, C. Kuhlemeier, Science 276, 1415 (1997)
Y. Klein, E. Efrati, E. Sharon, Science 315, 1116 (2007)
E. Sharon, E. Efrati, Soft Matter 6, 5693 (2010)
D. Nielsen, Design Nature (WIT, Southampton, 2010)
L. Jin, S. Cai, Z. Suo, EPL 95, 64002 (2011)
J.Y. Sun, S. Xia, M.W. Moon, K.H. Oh, K.S. Kim, Proc. Royal Soc. London Ser. A 468, 932 (2012)
F.S. Jeng, K.P. Huang, J. Struct. Geol. 30, 633 (2008)
S. Gyasi, R.B. Fridley, P. Chen, ASABE 24, 747 (1981)
C. Wei, P.M. Lintilhac, Plant Physiol. 145, 763 (2007)
L.J. Gibson, M.F. Ashby, K.E. Easterling, J. Mater. Sci. 23, 3041 (1988)
J.H. Heinbockel, Introduction to Tensor Calculus and Continuum Mechanics (Trafford, Victoria, 2001)
D.J. Beebe, J.S. Moore, J.M. Bauer, Q. Yu, R.H. Liu, C. Devadoss, B.H. Jo, Nature 404, 588 (2000)
T. Miyata, N. Asami, T. Uragami, Nature 399, 766 (1999)
W.R. Drummond, M.L. Knight, M.L. Brannon, N.A. Peppas, J. Controlled Release 7, 181 (1988)
M. Abendroth, M. Kuna, Comput. Mater. Sci. 28, 633 (2003)
R. Khalifehzadeha, S. Forouzanb, H. Aramib, S.K. Sadrnezhaad, Comput. Mater. Sci. 40, 359 (2007)
A. Paradis, P. Terriault, V. Brailovski, Comput. Mater. Sci. 47, 373 (2009)
S. Yang, K. Krishnacharya, P. Lin, Adv. Funct. Mater. 20, 2550 (2010)
J. Yin, X. Chen, J. Phys. D 43, 115402 (2010)
X. Chen, J. Yin, Soft Matter 6, 5667 (2010)
A. Schweikart, A. Fery, Microchim. Acta 165, 75 (2009)
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Yang, P., Zhang, C., Dang, F. et al. Abrupt out-of-plane edge folding of a circular thin plate: Implication for a mature Victoria regia leaf. Eur. Phys. J. E 39, 85 (2016). https://doi.org/10.1140/epje/i2016-16085-6
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DOI: https://doi.org/10.1140/epje/i2016-16085-6