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Thin sheets respond to confinement by smoothly wrinkling, or by focusingstress into small, sharp regions. From engineering to biology, geology,textiles, and art, thin sheets are packed and confined in a wide variety ofways, and yet fundamental questions remain about how stresses focus andpatterns form in these structures. Using experiments and molecular dynamics(MD) simulations, we probe the confinement response of circular sheets,flattened in their central region and quasi-statically drawn through a ring.Wrinkles develop in the outer, free region, then are replaced by a truncatedcone, which forms in an abrupt transition to stress focusing. We explore howthe force associated with this event, and the number of wrinkles, depend ongeometry. Additional cones sequentially pattern the sheet, until axisymmetry isrecovered in most geometries. The cone size is sensitive to in-plane geometry.We uncover a coarse-grained description of this geometric dependence, whichdiverges depending on the proximity to the asymptotic d-cone limit, where theclamp size approaches zero. This work contributes to the characterization ofgeneral confinement of thin sheets, while broadening the understanding of thed-cone, a fundamental element of stress focusing, as it appears in realisticsettings.

Wrinkling and developable cones in centrally confined sheets