5. A Kinetics Approach to Surface Wrinkling of Elastic Thin Films

Complex wrinkle patterns have been observed in various thin film systems, typically with integrated hard and soft materials for various applications as well as in nature. The underlying mechanism of wrinkling has been generally understood as a stress-driven instability. On an elastic substrate, equilibrium and energetics set the critical condition and select the wrinkle wavelength and amplitude. On a viscous substrate, wrinkles grow over time and kinetics select the fastest growing mode. Moreover, on a viscoelastic substrate, both energetics and kinetics play important roles in determining the critical condition, the growth rate, and wrinkle patterns. The dynamics of wrinkling, while analogous to other phase ordering phenomena, is rich and distinct under the effects of stress and film–substrate interactions. In this chapter, a kinetics approach is presented for wrinkling of isotropic and anisotropic elastic films on viscoelastic substrates. Analytic solutions are obtained by a linear perturbation analysis and a nonlinear energy minimization method, which predict the kinetics of wrinkle growth at the early stage and the equilibrium states at the long-time limit, respectively. In between, a power-law coarsening of the wrinkle wavelength is predicted by a scaling analysis. Furthermore, the kinetics approach enables numerical simulations that demonstrate emergence and transition of diverse wrinkle patterns (ordered and disordered) under various conditions.