# The Shape of Hanging Elastic Cylinders

## TL;DR

This paper investigates the equilibrium shapes and elastic instabilities of hanging elastic cylinders made of hydrogels under gravity, revealing pattern formations like wrinkling and hole development through experimental measurements.

## Contribution

It provides experimental evidence and analysis of shape transitions and elastic instabilities in heavy elastic cylinders, highlighting the critical parameters influencing pattern formation.

## Key findings

- Lateral wrinkling occurs beyond a critical deformation threshold.
- Holes form at the bottom surface in shallow samples.
- Pattern formation is driven by elastic instabilities.

## Abstract

Deformations of heavy elastic cylinders with their axis in the direction of earth's gravity field are investigated. The specimens, made of polyacrylamide hydrogels, are attached from their top circular cross section to a rigid plate. An equilibrium configuration results from the interplay between gravity that tends to deform the cylinders downwards under their own weight, and elasticity that resists these distortions. The corresponding steady state exhibits fascinating shapes which are measured with lab-based micro-tomography. For any given initial radius to height ratio, the deformed cylinders are no longer axially symmetric beyond a critical value of a control parameter that depends on the volume force, the height and the elastic modulus: lateral wrinkling hierarchy develops, and holes appear at the bottom surface of the shallowest samples. We show that these patterns are the consequences of elastic instabilities.