Disk wrinkling under gravity

TL;DR

This paper investigates how gravity causes a circular elastic disk to wrinkle, analyzing the critical conditions and the influence of geometry through experiments, simulations, and analytical methods.

Contribution

It introduces a new nondimensionalization of the transverse load to better understand the gravity-induced wrinkling instability in elastic disks.

Findings

Aspect ratio controls the instability threshold and mode.

A new nondimensional parameter captures the effect of gravity.

Experiments and simulations agree on the critical conditions.

Abstract

We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces a compressive orthoradial stresses which leads to a wrinkling instability above a critical threshold of the dimensionless gravity force. We study this instability by a combination of experiments, numerical simulations and analytical tools, with a particular focus on the role of geometry. We show that aspect ratio is a crucial parameter that controls both the threshold of instability and the most unstable mode. The influence of this parameter on the threshold can be catched by introducing a new nondimensionalization of the transverse load.