Dynamics of developable cones under shear

We identify and study a persistent structure characteristic of the post-buckling regime of a thin cylindrical shell subjected to axial torsion. It consists of a pair of developable cones ([Formula presented] cones) joined by an S-shaped ridge, having a size of the order of the radius of the cylinder. We study its formation by applying a concentrated load at the center of the shell, which creates an isolated pair of [Formula presented] cones, joined by a straight ridge that progressively tilts when a torsion angle is imposed. We interpret this response as the equilibrium state of a pair of interacting [Formula presented] cones in the presence of an in-plane shear field, created by axial torsion, which tends to drive them away from each other. We find that the amplitude of displacement of the [Formula presented] cones for a given torsion angle is amplified by decreasing the thickness of the sheet, therefore concluding that the equilibrium state is the result of a balance between bending and stretching energies. We propose a model where the driving effect is the coupling between the deformation field around the [Formula presented] cones and the imposed shear field, while the stabilizing effect is the increasing bending energy of the system.