A one-dimensional model for elasto-capillary necking

TL;DR

This paper develops a non-linear one-dimensional strain gradient model for predicting necking in soft elastic cylinders caused by surface tension, accurately capturing bifurcations and phase separation phenomena from 3D elasticity data.

Contribution

It introduces a novel 1D model derived from 3D elasticity that accurately predicts necking and bifurcations in soft elastic cylinders driven by surface tension.

Findings

The 1D model predicts bifurcations in necking behavior.

Finite-element comparisons show accurate interface resolution.

The model has a larger validity domain than previous models.

Abstract

We derive a non-linear one-dimensional (1d) strain gradient model predicting the necking of soft elastic cylinders driven by surface tension, starting from 3d finite-strain elasticity. It is asymptotically correct: the microscopic displacement is identified by an energy method. The 1d model can predict the bifurcations occurring in the solutions of the 3d elasticity problem when the surface tension is increased, leading to a localization phenomenon akin to phase separation. Comparisons with finite-element simulations reveal that the 1d model resolves the interface separating two phases accurately, including well into the localized regime, and that it has a vastly larger domain of validity than 1d model proposed so far.