Instability analysis of a programmed hydrogel plate under swelling

Abstract

We investigate the bifurcation instabilities of swelling circular hydrogel plates programed with a space-varying cross-linking density along the radial direction. Depending on the distribution of the cross-linking density and the aspect ratio of the plate, different buckling patterns are observed. When the cross-linking density is lower at the center and increases monotonically outwards, a global buckling occurs, and the hydrogel plate forms an axisymmetric bowl-shaped container. When the cross-linking density is higher at the center and decreases monotonically outwards, edge wrinkling occurs. These wrinkles can be either localized near the edge or penetrate deep into the plate, depending on the detailed distribution of the cross-linking density. The rich post-buckling morphologies exhibited by the programed hydrogel plate provide a powerful route to fabricate smart hydrogel components, such as, self-adjusting containers and microlenses.