Abstract: Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation fields, a new semi-analytical approach is developed to predict the swelling induced finite bending for a functionally graded (FG) layer composed of a pH-sensitive hydrogel, in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference, the initial state is mapped into the deformed configuration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the finite element method (FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement confirms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress fields are studied. Furthermore, the tangential free-stress axes are illustrated in deformed configuration.

Key words: convex metric spaces, (sub) compatible mapping, set-valued generalized nonexpansive mapping, common fixed points, semianalytical solution, finite element method (FEM), pH-sensitive hydrogel, finite bending, functionally graded (FG) layer