Gravity driven instability in elastic solids

TL;DR

This paper investigates the gravitational instability of the free surface of soft elastic solids, demonstrating a threshold at which surface patterns spontaneously form due to the interplay of gravity and elasticity.

Contribution

It provides experimental evidence and theoretical analysis of surface instability in elastic solids under gravity, identifying a critical parameter for pattern formation.

Findings

Surface remains flat below a critical threshold

Spontaneous pattern formation occurs above the threshold

Instability linked to the reduction of Rayleigh wave speed

Abstract

We demonstrate the instability of the free surface of a soft elastic solid facing downwards. Experiments are carried out using a gel of constant density $\rho$, shear modulus $\mu$, put in a rigid cylindrical dish of depth $h$. When turned upside down, the free surface of the gel undergoes a normal outgoing acceleration $g$. It remains perfectly flat for $\rho g h/\mu<\alpha^* $ with $\alpha^*\simeq 6$, whereas a steady pattern spontaneously appears in the opposite case. This phenomenon results from the interplay between the gravitational energy and the elastic energy of deformation, which reduces the Rayleigh waves celerity and vanishes it at the threshold.