title: Topological Mechanics of Origami and Kirigami.
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.
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
authors.forename: Bryan Gin-Ge
authors.initials: BG
authors.lastname: Chen
authors.affiliation: Department of Physics, Cornell University, NewYork 14853, USA.
authors.forename: Bin
authors.initials: B
authors.lastname: Liu
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, Massachusetts 01002, USA.
authors.forename: Arthur A
authors.initials: AA
authors.lastname: Evans
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
authors.forename: Jayson
authors.initials: J
authors.lastname: Paulose
authors.affiliation: Department of Physics, Cornell University, NewYork 14853, USA.
authors.forename: Itai
authors.initials: I
authors.lastname: Cohen
authors.affiliation: Instituut-Lorentz, Universiteit Leiden, 2300 RA Leiden, The Netherlands.
authors.forename: Vincenzo
authors.initials: V
authors.lastname: Vitelli
authors.affiliation: Department of Physics, University of Massachusetts, Amherst, Massachusetts 01002, USA.
authors.forename: C D
authors.initials: CD
authors.lastname: Santangelo