Intricate evolutions of multiple-period post-buckling patterns in bilayers

Surface instability of compliant film/substrate bilayers has raised considerable interests due to its broad applications such as wrinkle-driven surface renewal and antifouling,shape-morphing for camouflaging skins,and micro/nano-scale surface patterning control.However,it is still a challenge to precisely predict and continuously trace secondary bifurcation transitions in the nonlinear post-buckling region.Here,we develop lattice models to precisely capture the nonlinear morphology evolution with multiple mode transitions that occur in the film/substrate systems.Based on our models,we reveal an intricate post-buckling phenomenon involving successive flat-wrinkle-doubling-quadrupling-fold bifurcations.Pre-stretch and pre-compression of the substrate,as well as bilayer modulus ratio,can alter surface morphology of film/substrate bilayers.With high substrate pre-tension,hierarchical wrinkles emerge in the bilayer with a low modulus ratio,while a wrinkle-to-ridge transition occurs with a high modulus ratio.Besides,with moderate substrate pre-compression,the bilayer eventually evolves into a period-tripling mode.Phase diagrams based on neo-Hookean and Arruda-Boyce constitutions are drawn to characterize the influences of different factors and to provide an overall view of ultimate pattern formation.Fundamental understanding and quantitative prediction of the nonlinear morphological transitions of soft bilayer materials hold potential for multifunctional surface regulation.