title: Confined disclinations: exterior versus material constraints in developable thin elastic sheets.
abstract: We examine the shape change of a thin disk with an inserted wedge of material when it is pushed against a plane, using analytical, numerical, and experimental methods. Such sheets occur in packaging, surgery, and nanotechnology. We approximate the sheet as having vanishing strain, so that it takes a conical form in which straight generators converge to a disclination singularity. Then, its shape is that which minimizes elastic bending energy alone. Real sheets are expected to approach this limiting shape as their thickness approaches zero. The planar constraint forces a sector of the sheet to buckle into the third dimension. We find that the unbuckled sector is precisely semicircular, independent of the angle δ of the inserted wedge. We generalize the analysis to include conical as well as planar constraints and thereby establish a law of corresponding states for shallow cones of slope ε and thin wedges. In this regime, the single parameter δ/ε^{2} determines the shape. We discuss the singular limit in which the cone becomes a plane, and the unexpected slow convergence to the semicircular buckling observed in real sheets.
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science. PO Box 26, Rehovot, 76100, Israel.|James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.
authors.forename: Efi
authors.initials: E
authors.lastname: Efrati
authors.affiliation: James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.|Department of Surgery, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania 15261, USA.
authors.forename: Luka
authors.initials: L
authors.lastname: Pocivavsek
authors.affiliation: James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.|Departamento de Fisica de la Universidad de Santiago de Chile, av. Ecuador 3493, Santiago, 9170124, Chile.
authors.forename: Ruben
authors.initials: R
authors.lastname: Meza
authors.affiliation: James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.|Department of Chemistry, The University of Chicago, 929 E. 57th Street, Chicago, Illinois 60637, USA.
authors.forename: Ka Yee C
authors.initials: KY
authors.lastname: Lee
authors.affiliation: James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.
authors.forename: Thomas A
authors.initials: TA
authors.lastname: Witten
mesh_terms: D003198:Computer Simulation; D004548:Elasticity; D008962:Models, Theoretical