TY - JOUR
T1 - Topological transitions in the configuration space of non-Euclidean origami
AU - Berry, M.
AU - Lee-Trimble, M. E.
AU - Santangelo, C. D.
N1 - Funding Information:
We acknowledge funding from the National Science Foundation under Grant No. NSF DMR-1822638 and useful conversations with D. W. Atkinson, Z. Rocklin. and B. Chen. This work was done in part at the Aspen Center for Physics under Grant No. NSF PHY-1607611. M.E.L.-T. acknowledges funding from the National Science Foundation Graduate Research Fellowship Program, Award No. 451512 and the Spaulding-Smith Fellowship.
Publisher Copyright:
© 2020 American Physical Society.
PY - 2020/4
Y1 - 2020/4
N2 - Origami structures have been proposed as a means of creating three-dimensional structures from the micro-to the macroscale and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices, for arbitrary origami fold patterns. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. As an application of our general results, we show that the configuration space of nonintersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remains connected. This provides a new, and only partially explored, mechanism by which the mechanics and folding of an origami structure could be controlled.
AB - Origami structures have been proposed as a means of creating three-dimensional structures from the micro-to the macroscale and as a means of fabricating mechanical metamaterials. The design of such structures requires a deep understanding of the kinematics of origami fold patterns. Here we study the configurations of non-Euclidean origami, folding structures with Gaussian curvature concentrated on the vertices, for arbitrary origami fold patterns. The kinematics of such structures depends crucially on the sign of the Gaussian curvature. As an application of our general results, we show that the configuration space of nonintersecting, oriented vertices with positive Gaussian curvature decomposes into disconnected subspaces; there is no pathway between them without tearing the origami. In contrast, the configuration space of negative Gaussian curvature vertices remains connected. This provides a new, and only partially explored, mechanism by which the mechanics and folding of an origami structure could be controlled.
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U2 - 10.1103/PhysRevE.101.043003
DO - 10.1103/PhysRevE.101.043003
M3 - Article
C2 - 32422808
AN - SCOPUS:85084533706
SN - 1063-651X
VL - 101
JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
IS - 4
M1 - 043003
ER -