Onset of swell-induced surface instability of hydrogel layers with depth-wise graded material properties

A rich variety of instability patterns have been observed on the surface of hydrogel layers with depth-wise variation in material properties. In this paper, a state space method and a finite difference method are developed to predict the critical condition for onset of surface instability for hydrogel layers with continuously graded material properties in the thickness direction. Both methods are benchmarked by comparing to analytical solutions for homogeneous hydrogel layers and hydrogel bilayers. While the finite difference method often requires a large number of nodes to achieve convergence, the state space method requires relatively fewer sub-layers for continuously graded layers. The results for linearly and exponentially graded hydrogel layers show that the critical swelling ratio and corresponding critical wavelength both depend on the gradient profile of the crosslink density. The present study may provide theoretical guidance for analyzing and designing surface instability and surface patterns in hydrogel layers.