Curvature condensation and bifurcation in an elastic shell

TL;DR

This paper investigates how localized defects form and evolve in an elastic shell under indentation, revealing a transition from global to localized deformation, curvature condensation, and bifurcation phenomena through experiments and simulations.

Contribution

It introduces a combined experimental and numerical analysis of defect formation in shells, highlighting the transition mechanisms and bifurcation behavior of localized curvature defects.

Findings

Curvature condenses into a parabolic crease during indentation.

A soft mode emerges, transforming the shell into a hinged mechanism.

Bifurcation leads to twin creases moving apart symmetrically.

Abstract

We study the formation and evolution of localized geometrical defects in an indented cylindrical elastic shell using a combination of experiment and numerical simulation. We find that as a symmetric localized indentation on a semi-cylindrical shell increases, there is a transition from a global mode of deformation to a localized one which leads to the condensation of curvature along a symmetric parabolic crease. This process introduces a soft mode in the system, converting a load-bearing structure into a hinged, kinematic mechanism. Further indentation leads to twinning wherein the parabolic crease bifurcates into two creases that move apart on either side of the line of symmetry. A qualitative theory captures the main features of the phenomena and leads to sharper questions about the nucleation of these defects.