Effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes

Abstract

In this study, we investigate the effect of geometrical imperfections on swelling-induced buckling patterns in gel films with a square lattice of holes. Finite element analysis is performed using the inhomogeneous field theory of polymeric gels in equilibrium proposed by Hong et al. (2009). Periodic units consisting of 2×2 and 10×10 unit cells are analyzed under a generalized plane strain assumption. Geometrical imperfections are introduced using randomly oriented elliptical holes. The 2×2 unit cells show that the resulting buckling patterns are sensitive to imperfections; three different buckling patterns are obtained, and the most dominant one is the diamond plate pattern observed in experiments, which cannot be described using the model without imperfections. The 10×10 unit cells reveal that random imperfections are responsible for inducing homogeneous transformation into the diamond plate pattern. Furthermore, domain wall formation is simulated using a 10×10 unit cell model containing two elliptic holes.