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Oshri O, Brau F, Diamant H. Wrinkles and folds in a fluid-supported sheet of finite size. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(5):052408doi: 10.1103/PhysRevE.91.052408.
Oshri, O., Brau, F., & Diamant, H. (2015). Wrinkles and folds in a fluid-supported sheet of finite size. Physical review. E, Statistical, nonlinear, and soft matter physics, 91(5), 052408. https://doi.org/10.1103/PhysRevE.91.052408
Oshri, Oz, et al. "Wrinkles and folds in a fluid-supported sheet of finite size." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 91,5 (2015): 052408. doi: https://doi.org/10.1103/PhysRevE.91.052408
Oshri O, Brau F, Diamant H. Wrinkles and folds in a fluid-supported sheet of finite size. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052408. doi: 10.1103/PhysRevE.91.052408. Epub 2015 May 29. PMID: 26066184.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 May;91(5):052408. doi: 10.1103/PhysRevE.91.052408. Epub 2015 May 29.

Wrinkles and folds in a fluid-supported sheet of finite size.

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

Oz Oshri, Fabian Brau, Haim Diamant

Affiliations

  1. Raymond & Beverly Sackler School of Physics & Astronomy, Tel Aviv University, Tel Aviv 6997801, Israel.
  2. Nonlinear Physical Chemistry Unit, Université libre de Bruxelles (ULB), CP231, B-1050 Brussels, Belgium.
  3. Raymond & Beverly Sackler School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel.

PMID: 26066184 DOI: 10.1103/PhysRevE.91.052408

Abstract

A laterally confined thin elastic sheet lying on a liquid substrate displays regular undulations, called wrinkles, characterized by a spatially extended energy distribution and a well-defined wavelength λ. As the confinement increases, the deformation energy is progressively localized into a single narrow fold. An exact solution for the deformation of an infinite sheet was previously found, indicating that wrinkles in an infinite sheet are unstable against localization for arbitrarily small confinement. We present an extension of the theory to sheets of finite length L, accounting for the experimentally observed wrinkle-to-fold transition. We derive an exact solution for the periodic deformation in the wrinkled state, and an approximate solution for the localized, folded state. We find that a second-order transition between these two states occurs at a critical confinement Δ(F)=λ(2)/L.

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