Exact solutions for the wrinkle patterns of confined elastic shells
arXiv:2004.02839 · doi:10.1038/s41567-022-01672-2
Abstract
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive way of generating reconfigurable patterned topographies, but controlling the often asymmetric and apparently stochastic wrinkles that result remains an elusive goal. Here, we describe a new approach to understanding the wrinkles of confined elastic shells, using a Lagrange multiplier in place of stress. Our theory reveals a simple set of geometric rules predicting the emergence and layout of orderly wrinkles, and explaining a surprisingly generic co-existence of ordered and disordered wrinkle domains. The results agree with numerous test cases across simulation and experiment and represent an elementary geometric toolkit for designing complex wrinkle patterns.
arXiv commentThis version of the article has been accepted for publication, after peer review and is subject to Springer Nature's AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://doi.org/10.1038/s41567-022-01672-2
References in corpus (16)
- Non-uniform growth and surface friction determine bacterial biofilm morphology on soft substrates
- In-drop capillary spooling of spider capture thread inspires hybrid fibers with mixed solid-liquid mechanical properties
- Water affects morphogenesis of growing aquatic plant leaves
- Stamping and wrinkling of elastic plates
- Indentation of ultrathin elastic films and the emergence of asymptotic isometry
- Geometrically incompatible confinement of solids
- A sheet on deformable sphere: "wrinklogami" patterns suppress curvature-induced delamination
- Wrapping liquids, solids, and gases in thin sheets
- Regimes of wrinkling in pressurized elastic shells
- Geometry-driven folding of a floating annular sheet
- Isometric immersions, energy minimization and self-similar buckling in non-Euclidean elastic sheets
- Non-uniform Curvature and Anisotropic Deformation Control Wrinkling Patterns on Tori
- Wrinkling of a thin circular sheet bonded to a spherical substrate
- Curvature-driven wrinkling of thin elastic shells
- Mesoscale structure of wrinkle patterns and defect-proliferated liquid crystalline phases
- Sculpting liquids with ultrathin shells