A semi-analytical solution for finite bending of a functionally graded hydrogel strip

In this paper, a semi-analytical formulation is developed to examine the swelling-induced finite bending of a functionally graded hydrogel strip, when the strip is embedded in a solvent bath of an assigned chemical potential. The cross-link density of the hydrogel polymeric network varies through the strip thickness either linearly or exponentially. As a result of inhomogeneous swelling ratio through the hydrogel strip thickness, the strip bends in a circle. In contrast to earlier solution methods, the initial configuration is mapped to the deformed state without assuming any intermediary virtual state, using a total deformation gradient tensor. The swelling response of the hydrogel is studied utilizing the Flory–Huggins model for the free energy changes due to the mixing and deformation of the hydrogel network. In order to validate the presented method, FEM is employed to solve the finite bending of the functionally graded hydrogel strip. Using the presented method, the effects of the hydrogel network cross-link density distribution on the radial and tangential stress fields, strip bending curvature, and semi-angle are studied. In contrast to hydrogel-based multilayers, continuous stress and deformation field are found for the functionally graded hydrogel strip. Also, multiple tangential stress-free axes are observed for functionally graded hydrogel strips under bending configuration.