Harnessing Eversion Buckling for Ideal Omnidirectional Energy Absorption

Abstract

Thin shells can undergo large shape changes governed by the competition between bending and membrane energies. Here, we identify an instability mechanism in everted toroidal shells, referred to as eversion buckling. After eversion, the axisymmetric configuration may either remain stable or lose stability through symmetry breaking, depending on geometry. A scaling analysis reveals a dimensionless parameter that characterizes the ratio between membrane and bending energies. This parameter defines a critical threshold separating a bistable regime, where the axisymmetric everted state persists, from a monostable regime, where the shell collapses into a non-axisymmetric configuration. The transition is consistent with a pitchfork-type bifurcation, leading to collapse without a preferred in-plane direction. Finite element simulations and experiments validate the proposed scaling and the associated stability boundary across different shell geometries. In the bistable regime, individual everted shells exhibit rapid snap-through accompanied by large volumetric contraction and show limited sensitivity of the critical response to boundary constraints. Building on this mechanism, assemblies of such shells form granular systems with a stable stress plateau and high energy absorption efficiency. These results provide a mechanics-based framework for designing shell-based systems with robust and direction-insensitive energy absorption.