Wrinkling induced by poking a free-floating film under tension*

We study experimentally and theoretically the out-of-plane deformation in a floating polystyrene film induced by depressing the centre of the film by a distance, d. When this depth exceeds a critical value d{\_}c, the smooth conical deformation of the film becomes unstable to an elastic instability in which a radial wrinkling pattern develops. The wrinkles have a finite length, and originate a finite radius from the centre. This observation is completely reproduced by a calculation starting from the von Karman equations. Experimental results and theoretical predictions for the critical depth as a function of the thickness and elasticity of the films are in good agreement. We also present theoretical results for the number and the length of the wrinkles, and the radius of the cone of smooth deformation.