A basic characteristic of stiff film/soft substrate systems is their ability to experience large deformation under compressive stresses, which inevitably leads to formation of patterns on the surface. Such pattern formation is the result of loss of stability and symmetry breaking. Knowledge on how such instabilities arise and evolve is essential to describe, understand, predict, and ultimately to design complex functional materials and structures, for example the fabrication of stretchable electronic devices and microano-scale surface patterning control. In this paper, quantitative predictions of various instability pattern formations and evolutions, which involve highly nonlinear deformation and multiple bifurcations, will be presented based on advanced mechanical models and methods, from planar to curved geometry. The results can provide further insight into fundamental understanding in a whole view of a variety of surface patterning morphology and imply a potential way to facilitate the design of functional materials and structures by quantitatively harnessing surface instabilities.
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