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Dipoles in thin sheets

  • Jemal Guven
  • J. A. Hanna
  • Osman Kahraman
  • Martin Michael Müller
Regular Article

Abstract

A flat elastic sheet may contain pointlike conical singularities that carry a metrical “charge” of Gaussian curvature. Adding such elementary defects to a sheet allows one to make many shapes, in a manner broadly analogous to the familiar multipole construction in electrostatics. However, here the underlying field theory is non-linear, and superposition of intrinsic defects is non-trivial as it must respect the immersion of the resulting surface in three dimensions. We consider a “charge-neutral” dipole composed of two conical singularities of opposite sign. Unlike the relatively simple electrostatic case, here there are two distinct stable minima and an infinity of unstable equilibria. We determine the shapes of the minima and evaluate their energies in the thin-sheet regime where bending dominates over stretching. Our predictions are in surprisingly good agreement with experiments on paper sheets.

Graphical abstract

Keywords

Soft Matter: Interfacial Phenomena and Nanostructured Surfaces 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jemal Guven
    • 1
  • J. A. Hanna
    • 2
  • Osman Kahraman
    • 3
  • Martin Michael Müller
    • 3
    • 4
  1. 1.Instituto de Ciencias NuclearesUniversidad Nacional Autónoma de MéxicoMéxico D.F.México
  2. 2.Department of Engineering Science and MechanicsVirginia Polytechnic Institute and State University, Norris Hall (MC 0219)BlacksburgUSA
  3. 3.Equipe BioPhysStat, ICPMB-FR CNRS 2843Université de LorraineMetzFrance
  4. 4.Institut Charles SadronCNRSStrasbourgFrance

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