2010/09/13 by Haim Diamant, Thomas A. Witten, Diamant, Haim +1
Engineering · Physics and Astronomy · #Advanced Materials and Mechanics #FOS: Physical sciences #Micro and Nano Robotics #Soft Condensed Matter (cond-mat.soft) #Structural Analysis and Optimization #cond-mat.soft
paper · pdf · doi:10.48550/arxiv.1009.2487
8 pages; important comment added at the beginning
openalex publication_date 2010/09/13 · arxiv created 2011/07/28 · arxiv updated 2011/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We analyze the buckling of a rigid thin membrane floating on a dense fluid substrate. The interplay of curvature and substrate energy is known to create wrinkling at a characteristic wavelength λ, which localizes into a fold at sufficient buckling displacement Δ. By analyzing the regime Δ<<λ, we show that wrinkles are unstable to localized folding for \em arbitrarily small Δ. After observing that evanescent waves at the boundaries can be energetically favored over uniform wrinkles, we construct a localized Ansatz state far from boundaries that is also energetically favored. The resulting surface pressure P in conventional units is 2-(π2/4)(Δ/λ)2, in entire agreement with previous numerical results. The decay length of the amplitude is κ-1=(2/π2)λ2/Δ. This case illustrates how a leading-order energy expression suggested by the infinitesimal displacement can give a qualitatively wrong configuration.