Wrinkling of an elastic sheet floating on a liquid sphere

Abstract

A thin circular elastic sheet floating on a drop-like liquid substrate is deformed due to incompatibility between the curved substrate and the planar sheet. We adopt a variational viewpoint by minimizing the non-convex membrane energy together with a higher-order convex bending energy. Focusing on thin sheets, we expand the minimum of the energy in terms of a small thickness ratio $h$, and identify the first two terms of this expansion. The leading-order term arises from the minimization of a family of one-dimensional relaxed problems, while for the next-order term we establish lower and upper bounds. This generalizes the previous work [P. Bella and R.V. Kohn. Wrikling of a thin circular sheet bonded to a spherical substrate, Philos. Trans. Roy. Soc. A, 375(2017). arXiv:1611.01781] to the physically relevant case of a liquid substrate.

arXiv comment41 pages; version accepted for publication

References in corpus (15)

• Wrapping an adhesive sphere with a sheet
• Geometrically incompatible confinement of solids
• A sheet on deformable sphere: "wrinklogami" patterns suppress curvature-induced delamination
• Delamination from an adhesive sphere: Curvature-induced dewetting versus buckling
• Energy Bounds for a Compressed Elastic Film on a Substrate
• Rucks and folds: delamination from a flat rigid substrate under uniaxial compression
• Curvature-driven wrinkling of thin elastic shells
• Wrinkling of a thin circular sheet bonded to a spherical substrate
• Transition between planar and wrinkled regions in uniaxially stretched thin elastic film
• The shape of low energy configurations of a thin elastic sheet with a single disclination
• On a boundary value problem for conically deformed thin elastic sheets
• Axial compression of a thin elastic cylinder: bounds on the minimum energy scaling law
• 3D vortex approximation construction and $\epsilon$-level estimates for the Ginzburg-Landau functional
• On the first critical field in the 3D Ginzburg-Landau model of superconductivity
• Bounded vorticity for the 3D Ginzburg-Landau model and an isoflux problem