Mechanics of Wrinkled Structures

Surface wrinkling of thin films on soft substrates has been of great interest both in fundamental studies and in practical applications, such as tunable adhesion, wetting and drag coefficient. While the formation of wrinkles is well understood from the linear stability analysis, which can predict critical strains and buckled modes, we know much less how wrinkled structures respond to additional external forces. This is because post-buckled wrinkled surfaces are extremely sensitive and even small forces can lead to large deformations, which have to be described with the nonlinear elasticity. I will discuss how the corresponding nonlinear PDEs can be solved perturbatively, where the small parameter is the ratio between the magnitude of displacements (e.g. amplitude of wrinkles) with the wavelength of wrinkles (as determined from the linear elasticity). This way we can derive systematic estimates for the post-buckling response of wrinkled structures to external forces, such as a point indentation force or a point force directed in the plane of wrinkles. I will also comment how this formalism can be applied to analyze more complex interaction of the wrinkled structures with external environment, such as the effective wetting angle of liquid droplet on wrinkled surfaces.