Origami structures with a critical transition to bistability arising from hidden degrees of freedom.
Origami is used beyond purely aesthetic pursuits to design responsive and customizable mechanical metamaterials. However, a generalized physical understanding of origami remains elusive, owing to the challenge of determining whether local kinematic constraints are globally compatible and to an incomplete understanding of how the folded sheet's material properties contribute to the overall mechanical response. Here, we show that the traditional square twist, whose crease pattern has zero degrees of freedom (DOF) and therefore should not be foldable, can nevertheless be folded by accessing bending deformations that are not explicit in the crease pattern. These hidden bending DOF are separated from the crease DOF by an energy gap that gives rise to a geometrically driven critical bifurcation between mono- and bistability. Noting its potential utility for fabricating mechanical switches, we use a temperature-responsive polymer-gel version of the square twist to demonstrate hysteretic folding dynamics at the sub-millimetre scale.
Physics Department, Cornell University, Ithaca, New York 14853, USA.
Jesse L
JL
Silverberg
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Jun-Hee
JH
Na
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Arthur A
AA
Evans
Physics Department, Cornell University, Ithaca, New York 14853, USA.
Bin
B
Liu
Department of Mathematics, Western New England University, Springfield, Massachusetts 01119, USA.
Thomas C
TC
Hull
Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Christian D
CD
Santangelo
Lang Origami, Alamo, California 94507, USA.
Robert J
RJ
Lang
Department of Polymer Science and Engineering, University of Massachusetts, Amherst, Massachusetts 01003, USA.
Ryan C
RC
Hayward
Physics Department, Cornell University, Ithaca, New York 14853, USA.
Itai
I
Cohen
D001672:Biocompatible Materials / Q000737:chemistry*; D001696:Biomechanical Phenomena; D017076:Computer-Aided Design; D004355:Drug Stability; D005782:Gels / Q000737:chemistry; D021621:Imaging, Three-Dimensional; D008422:Materials Testing; D008958:Models, Molecular; D008968:Molecular Conformation; D015394:Molecular Structure; D011108:Polymers / Q000737:chemistry; D013816:Thermodynamics
D001672:Biocompatible Materials; D005782:Gels; D011108:Polymers