Finite bending of bilayer pH-responsive hydrogels: A novel analytic method and finite element analysis

Recently bilayer smart hydrogel beams are widely used in various applications such as sensors, actuators, self-folding structures and switches. Developing a strong tool for designing these bilayer smart hydrogel beams is necessary. In this article, we developed an analytical method to solve the swelling induced bending of bilayer beams made of a pH-sensitive layer attached to an inert elastomer layer. A total deformation gradient tensor, without assuming any intermediary virtual state, is defined to map the initial configuration to the deformed state. An exponential function with four constants is employed to describe the deformation of the pH-sensitive gel layer. The proposed method leads to a system of equations with six unknowns that can be simply solved via numerical techniques. As a case study, this method is implemented to solve the swelling induced bending of several bilayer beams with various parameters. The outcomes of the analytical solution are in excellent agreement with the finite element method results, thus confirming the strength of the presented method.