Buckling of Spherical Capsules

TL;DR

This study models the buckling behavior of soft elastic spherical capsules under negative pressure or volume reduction, revealing complex bifurcation patterns and stable shapes, with implications for experimental elastic modulus determination.

Contribution

It introduces a nonlinear shell theory-based numerical framework for analyzing capsule buckling, highlighting differences between prescribed volume and pressure conditions.

Findings

Buckled shapes are energetically favorable at smaller negative pressures.

Distinct bifurcation sequences occur for prescribed volume versus pressure.

A relation between curvature at the rim and bending modulus enables elastic property estimation.

Abstract

We investigate buckling of soft elastic capsules under negative pressure or for reduced capsule volume. Based on nonlinear shell theory and the assumption of a hyperelastic capsule membrane, shape equations for axisymmetric and initially spherical capsules are derived and solved numerically. A rich bifurcation behavior is found, which is presented in terms of bifurcation diagrams. The energetically preferred stable configuration is deduced from a least-energy principle both for prescribed volume and prescribed pressure. We find that buckled shapes are energetically favorable already at smaller negative pressures and larger critical volumes than predicted by the classical buckling instability. By preventing self-intersection for strongly reduced volume, we obtain a complete picture of the buckling process and can follow the shape from the initial undeformed state through the buckling instability into the fully collapsed state. Interestingly, the sequences of bifurcations and stable capsule shapes differ for prescribed volume and prescribed pressure. In the buckled state, we find a relation between curvatures at the indentation rim and the bending modulus, which can be used to determine elastic moduli from experimental shape analysis.