Wrinkling of a compressed elastic film on a viscous layer

A compressively strained elastic film bonded to a viscous layer can form wrinkles. The present study provides a theoretical model for the wrinkling process. The elastic film is modeled with the nonlinear theory of a thin plate subject to in-plane and out-of-plane loads. The flow of the viscous layer is modeled with the theory of lubrication. The interface between the elastic film and the viscous layer is assumed to be perfect with no slipping or debonding. A set of partial differential equations evolves the deflection and the in-plane displacements as functions of time. A linear stability analysis identifies the critical wave number, below which the elastic film is unstable and the wrinkles can grow. For any fixed wave number less than the critical wave number, the wrinkles reach a kinetically constrained equilibrium configuration, in which the stress is partially relaxed in the elastic film and the viscous layer stops flowing. Numerical simulations reveal rich dynamics of the system with many unstable equilibrium configurations.