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Topological Mechanics of Origami and Kirigami

Bryan Gin-ge Chen, Bin Liu, Arthur A. Evans, Jayson Paulose, Itai Cohen, Vincenzo Vitelli, and C. D. Santangelo
Phys. Rev. Lett. 116, 135501 – Published 30 March 2016
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Abstract

Origami and kirigami have emerged as potential tools for the design of mechanical metamaterials whose properties such as curvature, Poisson ratio, and existence of metastable states can be tuned using purely geometric criteria. A major obstacle to exploiting this property is the scarcity of tools to identify and program the flexibility of fold patterns. We exploit a recent connection between spring networks and quantum topological states to design origami with localized folding motions at boundaries and study them both experimentally and theoretically. These folding motions exist due to an underlying topological invariant rather than a local imbalance between constraints and degrees of freedom. We give a simple example of a quasi-1D folding pattern that realizes such topological states. We also demonstrate how to generalize these topological design principles to two dimensions. A striking consequence is that a domain wall between two topologically distinct, mechanically rigid structures is deformable even when constraints locally match the degrees of freedom.

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  • Received 5 August 2015

DOI:https://doi.org/10.1103/PhysRevLett.116.135501

© 2016 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied PhysicsInterdisciplinary Physics

Synopsis

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Topological Origami

Published 30 March 2016

Origami formed by folding and cutting a material can feature well-defined, tunable mechanical properties.

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Authors & Affiliations

Bryan Gin-ge Chen1,*, Bin Liu2,†, Arthur A. Evans3,‡, Jayson Paulose1, Itai Cohen2, Vincenzo Vitelli1, and C. D. Santangelo3

  • 1Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands
  • 2Department of Physics, Cornell University, NewYork 14853, USA
  • 3Department of Physics, University of Massachusetts, Amherst, Massachusetts 01002, USA

  • *Current Address: Department of Physics, University of Massachusetts, Amherst, MA 01002, USA.
  • Current Address: School of Natural Sciences, University of California, Merced, CA 95343, USA.
  • Current Address: Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.

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Issue

Vol. 116, Iss. 13 — 1 April 2016

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