Rim curvature anomaly in thin conical sheets revisited

Rim curvature anomaly in thin conical sheets revisited.

This paper revisits one of the puzzling behaviors in a developable cone (d-cone), the shape obtained by pushing a thin sheet into a circular container of radius R by a distance η. The mean curvature was reported to vanish at the rim where the d-cone is supported. We investigate the ratio of the two principal curvatures versus sheet thickness h over a wider dynamic range than was used previously...

Conical defects in growing sheets.

A growing or shrinking disc will adopt a conical shape, its intrinsic geometry characterized by a surplus angle phi(e) at the apex. If growth is slow, the cone will find its equilibrium. Whereas this is trivial if phi(e)0. We construct these states in the regime where bending dominates and determine their energi...

Formation of sprays from conical liquid sheets

Conical Kähler–Einstein Metrics Revisited

In this paper we introduce the “interpolation–degeneration” strategy to study Kähler–Einstein metrics on a smooth Fano manifold with cone singularities along a smooth divisor that is proportional to the anti-canonical divisor. By “interpolation” we show the angles in (0, 2π ] that admit a conical Kähler–Einstein metric form a connected interval, and by “degeneration” we determine the boundary o...

Localized Necking in Thin Sheets

SIJMMARY BY USING a simplified constitutive model of a pointed vertex on subsequent yield loci, namely, such that the equations of deformation-theory of rigid-plastic solids apply for fully-active stress increments, the onset of localized necking under biaxial stretching has been predicted. The predictions agree reasonably well with reported experimental observations. Since localized necking un...