Theoretical Analysis And Numerical Simulation Of Surface Wrinkling On General Curved Soft Materials

The instability of soft materials is related to the physical and chemical properties of the material surface.Understanding the mechanical mechanisms of the instability of soft materials is not only essential for understanding the formation of some wrinkling patterns in nature,but also guide us in designing some advanced functional materials,which have wide applications in modern technology.Although fruitful results have been achieved on surface wrinkling of thin films on flat and curved systems,theoretical and numerical research on wrinkling pattern evolution on a surface with curvature anisotropy and curvature gradient is still lacking.However,biological systems often possess surface curvature gradient,which may induce gradient wrinkling morphologies.Therefore,it is necessary to investigate the effect of curvature anisotropy and gradient on the wrinkling pattern transition in a bilayer curved system.Herein,we first briefly present types of instability,Koiter's elastic stability theory and the Fourier spectrum method.Then,theoretical analysis and numerical simulation on instability of soft material system with general curved surface based on Koiter's elasticity theory and the Fourier spectrum method are conducted,which mainly includes the following two parts:(1)A theoretical analysis method based on Koiter's elasticity theory is proposed to investigate wrinkling pattern evolution on a surface with curvature anisotropy and curvature gradient.The critical buckling analysis results indicate that the critical buckling mode of a bilayer curved system is sinusoidal,and the wrinkles at the critical state are perpendicular to the maximum curvature direction.Post-buckling analysis shows that dimensionless curvature and curvature anisotropy play a key role in wrinkling pattern transitions,i.e.,the sinusoidal–hexagonal transition point.(2)A Fourier spectral method is developed to track the surface wrinkling pattern evolution in a curved bilayer system based on the nonlinear equilibrium equations.The evolution sequence of the wrinkling pattern of a spherical system given from the Fourier spectral method are basically consistent with the wrinkling morphologies observed in past experiments.For more general curved systems with curvature anisotropy,a sinusoidal pattern is observed first and evolves into a hexagonal pattern very quickly as the excess stress increases.The hexagonal pattern further evolves into the bistable and ultimately into the labyrinth modes.This work may not only help understand some wrinkling pattern formation in some natural curved systems,but also find some potential applications,such as design of anti-counterfeiting systems.