# Dipoles in thin sheets

3 Equipe BioPhysStat
IJB - Institut Jean Barriol
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.
Document type :
Journal articles

https://hal.univ-lorraine.fr/hal-01513424
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Submitted on : Tuesday, April 25, 2017 - 10:20:23 AM
Last modification on : Thursday, May 7, 2020 - 1:38:14 AM

### Citation

Jemal Guven, J. A. Hanna, Osman Kahraman, Martin Michael Mueller. Dipoles in thin sheets. European Physical Journal E: Soft matter and biological physics, EDP Sciences: EPJ, 2013, 36 (9), ⟨10.1140/epje/i2013-13106-0⟩. ⟨hal-01513424⟩

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