Quantitative predictions of diverse wrinkling patterns in film/substrate systems
Résumé
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 micro/nano-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. Surface morphological instabilities of a soft material with a stiff thin surface layer have raised considerable research interests during past few years. Abundant examples can be found in various types of living creatures across length scales such as blooming process of hornbeam leaves 1 , hierarchical wrinkling of skins 2 and fi gers 3 , folding of growing tubular organs 4 and human brain development 5 , morphological buckling of fruits and vegetables 6–8 , and differential growth of bacterial biofilms 9. Besides, in modern industry, surface wrinkling can be widely applied in large area ranging from micro/nano morphological patterning control 10–12 , fabrication of fle-ible electronic devices 13,14 , mechanical self-assembly of islands on nano-particles 15 , defect localization in elastic surface crystals 16 , wet surface chemical patterning of micro-spheres 17 , multi-periodic surface topography of coated materials 18 , adaptive aerodynamic drag control 19,20 , mechanical property measurement of material characteristics 21 , to the design of moisture-responsive wrinkling devices with tunable dynamics 22 and reversible optical writing/erasure functional surface 23. These phenomena or functions with patterning morphology involve surface instability and symmetry breaking which are usually induced by large deformation of film/substrate systems under compressive stresses. Knowledge on how such instabilities arise and evolve is essential to describe, understand, predict, and ultimately to design complex functional materials and structures as listed above. Although linear perturbation analyses can predict the wrinkling wavelength at the initial stage of instability threshold, determining the post-bifurcation response and surface mode transition requires nonlinear buckling analyses. During post-buckling, the wavelength, amplitude and instability mode may vary with respect to external load. Due to its well-known complexity, most recent post-buckling analyses have recourse to computational approaches, especially through fin te element method 24–32 , since a limited number of exact analytical solutions can be obtained only in very simple or simplifi d cases 33. Nevertheless, surface instability of stiff layers attached on soft materials usually involves strong geometrical nonlinearities, large rotations, large displacements, loading path dependence, multiple symmetry-breakings, nonlinear constitutive relations, localizations and other complexities, which makes the numerical resolution quite difficult 33. The morphological post-buckling evolution and mode transition beyond the critical load are incredibly complicated, especially in 3D cases, and conventional numerical methods are limited in studying the post-bifurcation response on their complex evolution paths. Besides, several early works in the literature apply Fourier-based methods 34–36 , which prescribe periodic boundary conditions and cannot account for boundary effects on pattern evolution. A general model incorporating reliable and robust
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