Buckling of geometrically confined shells

TL;DR

This paper investigates how elastic shells buckle into various patterns under geometric confinement, revealing a key parameter that predicts the number of lobes and linking shell shape to boundary conditions.

Contribution

The study introduces a unified model that relates the buckling pattern to a single geometric parameter, extending it to account for in-plane constraint relaxation.

Findings

A single geometric parameter predicts lobe number in confined shells.

Reducing transverse confinement decreases the number of lobes as per the model.

Experimental and numerical data validate the effective stiffness model.

Abstract

We study the periodic buckling patterns that emerge when elastic shells are subjected to geometric confinement. Residual swelling provides access to range of shapes (saddles, rolled sheets, cylinders, and spherical sections) which vary in their extrinsic and intrinsic curvatures. Our experimental and numerical data show that when these structures are radially confined, a single geometric parameter -- the ratio of the total shell radius to the amount of unconstrained material -- predicts the number of lobes formed. We then generalize our model to account for a relaxation of the in-plane constraint by interpreting this parameter as an effective foundation stiffness. Experimentally, we show that reducing the transverse confinement of saddles causes the lobe number to decrease according to our effective stiffness model. Hence, one geometric parameter captures the wave number through a wide range of radial and transverse confinement, connecting the shell shape to the shape of the boundary that confines it. We expect these results to be relevant for an expanse of shell shapes, and thus apply to the design of shape--shifting materials and the swelling and growth of soft structures.