In this paper we analyze evolution of wrinkle patterns of anisotropic crystal films on viscoelastic substrates. The effects of the residual stress state in the film and the anisotropic elastic property are emphasized. Analytical solutions for the initial growth kinetics and the equilibrium states are presented along with numerical simulations based on nonlinear evolution equations. Compared to wrinkling of isotropic elastic films, more ordered wrinkle patterns are predicted, including orthogonal, zigzag, parallel, and checkerboard patterns. Tranistion of the wrinkle patterns under various stress states is elucidated. Some related experimental works are referred to, but quantitative comparisons between the model the experiments await further studies.

H. Mei, J.Y. Chung, H.-H. Yu, C.M. Stafford, and R. Huang, Buckling modes of elastic thin films on elastic substrates. Applied Physics Letters 90, 151902 (2007).

Two modes of thin film buckling are commonly observed, one with interface delamination (e.g., telephone cord blisters) and the other with no delamination (i.e., wrinkling). Which one would occur for your film?

This Letter gives a quantitative criterion for the selection of the buckling modes. An experiment with a polystyrene film on a PDMS substrate was described showing a transition of the buckling modes.

Rui Huang and Se Hyuk Im, Physical Review E 74, 026214 (2006).

A stressed thin film on a soft substrate can develop complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a simple scaling law under uniaxial compression. Slightly different dynamics is observed under equi-biaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a labyrinth pattern under equi-biaxial stresses. Both have the same wavelength, independent of the initial stress. On the other hand, the wrinkle amplitude depends on the initial stress state, which is higher under an equi-biaxial stress than that under a uniaxial stress of the same magnitude.

A recent discussion here about the effect of surface stress on vibrations of microcantilever has gained some interest from our members. A few years ago, Zhigang and I looked at surface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent with Wei Hong and Pradeep's comments toward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).