  Thin sheets respond to confinement by smoothly wrinkling, or by focusing
stress into small, sharp regions. From engineering to biology, geology,
textiles, and art, thin sheets are packed and confined in a wide variety of
ways, and yet fundamental questions remain about how stresses focus and
patterns 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 truncated
cone, which forms in an abrupt transition to stress focusing. We explore how
the force associated with this event, and the number of wrinkles, depend on
geometry. Additional cones sequentially pattern the sheet, until axisymmetry is
recovered in most geometries. The cone size is sensitive to in-plane geometry.
We uncover a coarse-grained description of this geometric dependence, which
diverges depending on the proximity to the asymptotic d-cone limit, where the
clamp size approaches zero. This work contributes to the characterization of
general confinement of thin sheets, while broadening the understanding of the
d-cone, a fundamental element of stress focusing, as it appears in realistic
settings.
