Disk wrinkling under gravity

We study the deflection by gravity of a circular elastic disk deposited on a rigid support. The axisymmetric deflection induces 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 caught by introducing a new nondimensionalization of the transverse load.