Abstract
Emergence of hierarchy during compression of quasi-planar bilayers is preceded by a mode-locked state during which the quasi-planar form persists. Transition to hierarchy is determined entirely by geometrically observable parameters. This results in a universal transition phase diagram that enables one to deterministically tune hierarchy even with limited knowledge about material properties.
Highlights
The MIT Faculty has made this article openly available
We have overcome this limitation for the specific case of hierarchical wrinkled patterns by demonstrating deterministic switching of hierarchy during compression of quasi-planar bilayers
We show that the emergence of hierarchy during compression of quasi-planar bilayers is determined by two competing effects that arise due to the non-flat periodic geometry of such systems
Summary
Several empirical studies have demonstrated the feasibility of hierarchical wrinkle formation by “adding up” patterns.[17,18,19,20,21] Physical pattern addition is often achieved by compressing a pre-patterned non-flat bilayer.[19,20,21] This non-flat geometry can be conveniently generated via recursive wrinkling, that is, by replicating/imprinting wrinkled patterns that are fabricated via compression of flat bilayers.[19] As wrinkled patterns form due to non-linear buckling bifurcation phenomena, the observed composite patterns are not equivalent to a linear superposition of the elementary patterns To predict these composite patterns, approximate semi-empirical models may be generated by reducing the prepatterned system to either a flat bilayer[21] or a curved bilayer with a non-zero average global curvature.[22] such approximations do not capture the physical effect of quasi-planar geometry on pattern formation. Emergence of hierarchy is preceded by a mode-locked state during which the quasiplanar form persists
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