Elasto-capillary necking, bulging and Maxwell states in soft compressible cylinders

TL;DR

This paper develops analytical conditions for localized deformation patterns like necking and bulging in soft, compressible cylinders under surface tension and axial load, linking bifurcation analysis with numerical simulations.

Contribution

It introduces a unified analytical framework for predicting localization and phase separation in soft cylinders, incorporating material compressibility and strain-stiffening effects.

Findings

Analytical bifurcation conditions match numerical results.

Material properties influence the bifurcation point.

Simple expressions describe the Maxwell state evolution.

Abstract

Localized pattern formations and "two-phase" deformations are studied theoretically in soft compressible cylinders subject to surface tension and axial loading through several force-controlled loading scenarios. By drawing upon known results for separate yet mathematically similar elastic localization problems, a concise family of analytical bifurcation conditions for localized bulging or necking are derived in terms of a general compressible strain energy function. The effect of material compressibility and strain-stiffening behaviour on the bifurcation point is analysed, and comparisons between our theoretical bifurcation conditions and the corresponding numerical simulation results of Dortdivanlioglu and Javili (Extreme Mech. Lett. 55, 2022) are made. It is then explained how the fully developed "two-phase" (Maxwell) state which evolves from the initial localized bifurcation solution can be comprehensively understood using the simple analytical expressions for the force parameters corresponding to the primary axial tension deformation. The power of this simple analytical approach in validating numerical simulation results for elastic localization and phase-separation-like problems of this nature is highlighted