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Efrati E, Pocivavsek L, Meza R, et al. Confined disclinations: exterior versus material constraints in developable thin elastic sheets. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(2):022404doi: 10.1103/PhysRevE.91.022404.
Efrati, E., Pocivavsek, L., Meza, R., Lee, K. Y., & Witten, T. A. (2015). Confined disclinations: exterior versus material constraints in developable thin elastic sheets. Physical review. E, Statistical, nonlinear, and soft matter physics, 91(2), 022404. https://doi.org/10.1103/PhysRevE.91.022404
Efrati, Efi, et al. "Confined disclinations: exterior versus material constraints in developable thin elastic sheets." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 91,2 (2015): 022404. doi: https://doi.org/10.1103/PhysRevE.91.022404
Efrati E, Pocivavsek L, Meza R, Lee KY, Witten TA. Confined disclinations: exterior versus material constraints in developable thin elastic sheets. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):022404. doi: 10.1103/PhysRevE.91.022404. Epub 2015 Feb 09. PMID: 25768515.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):022404. doi: 10.1103/PhysRevE.91.022404. Epub 2015 Feb 09.

Confined disclinations: exterior versus material constraints in developable thin elastic sheets.

Physical review. E, Statistical, nonlinear, and soft matter physics

Efi Efrati, Luka Pocivavsek, Ruben Meza, Ka Yee C Lee, Thomas A Witten

Affiliations

  1. Department of Physics of Complex Systems, Weizmann Institute of Science. PO Box 26, Rehovot, 76100, Israel.
  2. James Franck Institute, The University of Chicago, 929 E. 57th St., Chicago, Illinois 60637, USA.
  3. Department of Surgery, University of Pittsburgh Medical Center, Pittsburgh, Pennsylvania 15261, USA.
  4. Departamento de Fisica de la Universidad de Santiago de Chile, av. Ecuador 3493, Santiago, 9170124, Chile.
  5. Department of Chemistry, The University of Chicago, 929 E. 57th Street, Chicago, Illinois 60637, USA.

PMID: 25768515 DOI: 10.1103/PhysRevE.91.022404

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.

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