Bifurcation and deformation during the evolution of periodic patterns on a gel film bonded to a soft substrate

Abstract

In this study, we investigate the bifurcation and deformation during the evolution of periodic patterns on a gel film bonded to a soft substrate. 3D finite element analysis is performed using an inhomogeneous field theory for polymeric gels. Step-by-step eigenvalue buckling analysis is conducted to explore not only the first bifurcation, but also sequential bifurcations on bifurcated paths. When the hexagonal dimple mode occurs as the first bifurcation, the second bifurcation consists of rectangular checkerboard modes in three symmetric directions. The resulting deformation patterns are in good agreement with experiments and, surprisingly, are analogous to the in-plane buckling behavior of hexagonal honeycombs. Uniaxial, biaxial, and equibiaxial (flower-like) patterns are produced by the periodic arrangements of distorted dimples. The third and fourth bifurcations cause the coalescence of the selected dimples. This reveals the occurrence of the rectangular checkerboard modes at the second bifurcation to be the missing link in the pattern evolution from hexagonal dimples to herringbone and labyrinth patterns.