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Full-Text Articles in Physical Sciences and Mathematics
Mechanics Of Large Folds In Thin Interfacial Films, Vincent Demery, Benny Davidovitch, Christian Santangelo
Mechanics Of Large Folds In Thin Interfacial Films, Vincent Demery, Benny Davidovitch, Christian Santangelo
Christian Santangelo
A thin film confined to a liquid interface responds to uniaxial compression by wrinkling, and then by folding, that has been solved exactly before self-contact. Here, we address the mechanics of large folds, i.e., folds that absorb a length much larger than the wrinkle wavelength. With scaling arguments and numerical simulations, we show that the antisymmetric fold is energetically favorable and can absorb any excess length at zero pressure. Then, motivated by puzzles arising in the comparison of this simple model to experiments on lipid monolayers or capillary rafts, we discuss how to incorporate film weight, self-adhesion, or energy dissipation.
Nonuniform Growth And Topological Defects In The Shaping Of Elastic Sheets, Nakul Bende, Ryan C. Hayward, Christian Santangelo
Nonuniform Growth And Topological Defects In The Shaping Of Elastic Sheets, Nakul Bende, Ryan C. Hayward, Christian Santangelo
Christian Santangelo
We demonstrate that shapes with zero Gaussian curvature, except at singularities, produced by the growth-induced buckling of a thin elastic sheet are the same as those produced by the Volterra construction of topological defects in which edges of an intrinsically flat surface are identified. With this connection, we study the problem of choosing an optimal pattern of growth for a prescribed developable surface, finding a fundamental trade-off between optimal design and the accuracy of the resulting shape which can be quantified by the length along which an edge should be identified.