TY - JOUR

T1 - Wrinkles and folds in a fluid-supported sheet of finite size

AU - Oshri, Oz

AU - Brau, Fabian

AU - Diamant, Haim

N1 - Publisher Copyright:
©2015 American Physical Society.

PY - 2015/5/29

Y1 - 2015/5/29

N2 - 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 ΔF = λ2/L.

AB - 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 ΔF = λ2/L.

UR - http://www.scopus.com/inward/record.url?scp=84930637281&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.91.052408

DO - 10.1103/PhysRevE.91.052408

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AN - SCOPUS:84930637281

VL - 91

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

M1 - 052408

ER -