Dynamics of conical singularities: S type d-cones

Abstract

Conical singularities or tips of developable cones (d-cones) arising when thin sheets are subjected to large homogeneous deformations are very common but poorly understood structures. This paper reports on the nucleation and motion of these singularities in a cylindrical sheet deformed following a direction perpendicular to the principal cylinder axis. We show that in this geometry two opposite d- cones are generated. As deformation is increased d-cone tips move apart producing a change in the d-cone topology; from a regular d- cone to a type S d-cone. For metallic sheet, a moving tip gives rise to a wrinkle which is in fact one of the wings of a S type d-cone. By studying the motion of single d-cones tips in simple configurations, we conclude that any tip motion can be decomposed into two elementary processes: climbing and gliding. Both processes occur when forces along the d-cone generators, straight lines ending at d-cone tip, are not equilibrated. Thus, S d-cones can be seen as a natural consequence of a motion of d-cone tip involving both climbing and gliding.