TY - JOUR
T1 - Invariant and smooth limit of discrete geometry folded from bistable origami leading to multistable metasurfaces
AU - Liu, Ke
AU - Tachi, Tomohiro
AU - Paulino, Glaucio H.
N1 - Funding Information:
We thank the support from the US National Science Foundation (NSF) through grant no.1538830, the China Scholarship Council (CSC), and the Raymond Allen Jones Chair at Georgia Tech. The authors would like to extend their appreciation to Mrs. Emily D. Sanders for helpful discussions which contributed to improve the present work.
Publisher Copyright:
© 2019, The Author(s).
PY - 2019/12/1
Y1 - 2019/12/1
N2 - Origami offers an avenue to program three-dimensional shapes via scale-independent and non-destructive fabrication. While such programming has focused on the geometry of a tessellation in a single transient state, here we provide a complete description of folding smooth saddle shapes from concentrically pleated squares. When the offset between square creases of the pattern is uniform, it is known as the pleated hyperbolic paraboloid (hypar) origami. Despite its popularity, much remains unknown about the mechanism that produces such aesthetic shapes. We show that the mathematical limit of the elegant shape folded from concentrically pleated squares, with either uniform or non-uniform (e.g. functionally graded, random) offsets, is invariantly a hyperbolic paraboloid. Using our theoretical model, which connects geometry to mechanics, we prove that a folded hypar origami exhibits bistability between two symmetric configurations. Further, we tessellate the hypar origami and harness its bistability to encode multi-stable metasurfaces with programmable non-Euclidean geometries.
AB - Origami offers an avenue to program three-dimensional shapes via scale-independent and non-destructive fabrication. While such programming has focused on the geometry of a tessellation in a single transient state, here we provide a complete description of folding smooth saddle shapes from concentrically pleated squares. When the offset between square creases of the pattern is uniform, it is known as the pleated hyperbolic paraboloid (hypar) origami. Despite its popularity, much remains unknown about the mechanism that produces such aesthetic shapes. We show that the mathematical limit of the elegant shape folded from concentrically pleated squares, with either uniform or non-uniform (e.g. functionally graded, random) offsets, is invariantly a hyperbolic paraboloid. Using our theoretical model, which connects geometry to mechanics, we prove that a folded hypar origami exhibits bistability between two symmetric configurations. Further, we tessellate the hypar origami and harness its bistability to encode multi-stable metasurfaces with programmable non-Euclidean geometries.
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U2 - 10.1038/s41467-019-11935-x
DO - 10.1038/s41467-019-11935-x
M3 - Article
C2 - 31530802
AN - SCOPUS:85072297438
SN - 2041-1723
VL - 10
JO - Nature Communications
JF - Nature Communications
IS - 1
M1 - 4238
ER -