Elastic Platonic Shells

TL;DR

This paper demonstrates how defect control on elastic spherical shells can induce sharp buckling transitions to Platonic solid shapes, offering a new method for shape engineering in soft materials.

Contribution

It introduces a novel approach to shape control of elastic shells through defect topology and develops a Landau theory to describe the buckling transition.

Findings

Defects induce sharp buckling transitions from spherical to Platonic shapes.

The transition exhibits strong hysteresis during loading and unloading.

A minimal Landau theory captures the transition dynamics.

Abstract

On microscopic scales, the crystallinity of flexible tethered or cross linked membranes determines their mechanical response. We show that by controlling the type, number and distribution of defects on a spherical elastic shell, it is possible to direct the morphology of these structures. Our numerical simulations show that by deflating a crystalline shell with defects, we can create elastic shell analogs of the classical Platonic solids. These morphologies arise via a sharp buckling transition from the sphere which is strongly hysteretic in loading-unloading. We construct a minimal Landau theory for the transition using quadratic and cubic invariants of the spherical harmonic modes. Our approach suggests methods to engineer shape into soft spherical shells using a frozen defect topology.