A numerical study of the wrinkling evolution of an elastic film on a viscous layer

Abstract

The wrinkling phenomenon of a compressed elastic thin film bonded to a viscous layer is studied. Linear stability analysis (LSA) shows that, for materials with cubic crystalline symmetry, the sign of the degree of elastic anisotropy ζ = ((C12 + 2C44)/C11) − 1 plays an important role in the anisotropy of the buckling instability of the thin film system. More precisely, the growth rate of the fastest growing wave number, taken as a function of directions, reaches a peak in the ⟨1 0 0⟩ directions for ζ > 0 and in the ⟨1 1 0⟩ directions for ζ < 0. A highly efficient semi-implicit spectral method is established. The numerical experiments of long time wrinkling evolution processes of a 1 + 2-dimensional system verified the LSA results, successfully simulated anisotropic wrinkling pattern formation and coarsening, produced a power law scaling and reproduced certain featured phenomena observed in physical experiments.