Negative Gaussian curvature regulated pattern evolution on curved bilayer system

Abstract

Diverse wrinkling patterns may occur on curved bilayer system under equi-biaxial compression. Here we study the wrinkling pattern evolution on curved bilayer system with negative Gaussian curvature via theoretical analysis and numerical simulations. Different with curved system with zero Gaussian curvature or positive Gaussian curvature, critical buckling analysis demonstrates that negative Gaussian curvature doesn't delay the occurrence of the surface wrinkling. Fourier spectral method, finite element simulations and post buckling analysis based on an upper-bound method have revealed three different evolutionary paths of the wrinkling patterns with the increase of the excess stress. Selection of the evolutionary path is determined by the dimensionless curvature and curvature anisotropy. The results in this work help understand the profound effect of curvature on surface wrinkling of bilayer systems, and provide a new means to regulate the wrinkling pattern and its evolutionary path on soft materials.