Wrinkle formations in axi-symmetrically stretched membranes.

We study experimentally the main features of wrinkles that form in an initially stretched and flat elastic membrane when subjected to an axi-symmetric traction force at the center. The wavelength and amplitude of the wrinkle pattern are accurately characterized as the membrane tension and the traction forced are varied. We show that wrinkles are the result of a supercritical instability and appear for a well-defined critical traction force that is a function of the membrane tension. Wrinkle length and amplitude increase as the traction force is increased further. By contrast, both quantities decrease as the membrane tension is increased. Calculations based on symmetry arguments and elastic-energy minimization are in good agreement with experiments and provide a simple way to investigate configurations that are difficult to access experimentally. Such problems include wrinkles in elastic nano-films on finite-thickness viscous substrates used in semiconductor technology or in cellular forces detection.