On the shape transformation of cone scales.

The shape-morphing behaviours of some biological systems have drawn considerable interest over many years. This paper divulges that the opening and closing mechanism of pine cones is attributed to the self-bending of their scales, which undergo three states of humidity-driven deformation in terms of Föppl-von Kármán plate theory. Both numerical simulation and experimental measurement support the theoretical analysis, showing that the longitudinal principal curvature and the transverse principal curvature bifurcate at a critical humidity level according to the thickness and shape of scales. These findings help us understand the shape transformation of bilayer or multi-layer natural structures and gain insights into the design of transformable devices/materials with great potential in numerous applications.

[1]  Meie Li,et al.  Modeling programmable deformation of self-folding all-polymer structures with temperature-sensitive hydrogels , 2013 .

[2]  Paul B. Reverdy,et al.  Capillary origami: spontaneous wrapping of a droplet with an elastic sheet. , 2006, Physical review letters.

[3]  Xi-Qiao Feng,et al.  Hierarchical chirality transfer in the growth of Towel Gourd tendrils , 2013, Scientific Reports.

[4]  K. Schulgasser,et al.  THE MECHANICS OF SEED EXPULSION IN ACANTHACEAE , 1995 .

[5]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[6]  Kiwoong Kim,et al.  Journey of water in pine cones , 2015, Scientific Reports.

[7]  David H. Gracias,et al.  Curving Nanostructures Using Extrinsic Stress , 2010, Advanced materials.

[8]  Huajian Gao,et al.  Surface wrinkling patterns on a core-shell soft sphere. , 2011, Physical review letters.

[9]  S. Timoshenko,et al.  Analysis of Bi-Metal Thermostats , 1925 .

[10]  Z. Cao,et al.  Stressed Fibonacci spiral patterns of definite chirality , 2007 .

[11]  E. H. Mansfield.  The Bending and Stretching of Plates , 1963 .

[12]  J. Retana,et al.  Role of heat tolerance and cone protection of seeds in the response of three pine species to wildfires , 1999, Plant Ecology.

[13]  David H. Gracias,et al.  Self-folding thin-film materials: From nanopolyhedra to graphene origami , 2012 .

[14]  L. Mahadevan,et al.  How the Venus flytrap snaps , 2005, Nature.

[15]  I. Stewart.  Mathematics: Some assembly needed , 2007, Nature.

[16]  Amar J. S. Klar.  Plant mathematics: Fibonacci's flowers , 2002, Nature.

[17]  Jeong-Hyun Cho,et al.  Self-Assembly Based on Chromium/Copper Bilayers , 2009, Journal of Microelectromechanical Systems.

[18]  C. Dawson,et al.  How pine cones open , 1997, Nature.

[19]  Leonid Ionov,et al.  Biomimetic 3D self-assembling biomicroconstructs by spontaneous deformation of thin polymer films , 2012 .

[20]  SiOx∕Si radial superlattices and microtube optical ring resonators , 2006, cond-mat/0611261.

[21]  Henry I. Smith,et al.  Membrane folding to achieve three-dimensional nanostructures: Nanopatterned silicon nitride folded with stressed chromium hinges , 2006 .

[22]  L. Mahadevan,et al.  The shape of a long leaf , 2009, Proceedings of the National Academy of Sciences.

[23]  André R Studart,et al.  Bioinspired materials that self-shape through programmed microstructures. , 2014, Soft matter.