Modeling kinetics of diffusion-controlled surface wrinkles.

Nonlinear wrinkling of a compressed film on a soft substrate in the presence of inhomogeneous swelling actuation strain caused by solvent diffusion is studied. The simulation relies on a continuum model which integrates phase field microelasticity and Föppl-von Kármán plate theory. We show that the wrinkling morphologies developed in the diffusive domain exceeding a critical compression are confined and become shape and size dependent. A rich variety of wrinkling patterns observed in experiments including hexagonal ordered, dimple, or peanut structures, are numerically recovered, depending on the distribution of diffusion-mediated actuation strain. A cascade feature of the diffusion-coupled wrinkle is demonstrated as well: There are two ranges of solvent concentration within which the sequences of wrinkling pattern are different.