Analytic and Finite Element Studies on Deformation of Bilayers with a Functionally Graded PH-Responsive Hydrogel Layer

Abstract

Due to their wide application, responsive hydrogel bilayers have recently persuaded researchers to develop efficient tools to design these attractive structures. In this work, the deformation of a bilayer comprising a neutral elastomeric layer and a functionally graded (FG) pH-responsive one is investigated. The material properties of the FG hydrogel layer vary in the thickness direction. An analytical technique is developed to predict the behavior of the bilayer. To predict the pH-responsive layer behavior, a second-order ordinary differential equation (ODE) is formulated and solved such that the relevant boundary conditions are satisfied, resulting in solving the governing equations related to this layer. Also, for the under-study bilayer, numerical simulation of the considered problem is performed using the finite element method (FEM) — implementing a user-defined subroutine of UHYPER — through ABAQUS. The bending semi-angle, radial, and tangential stresses of the bilayer are studied in some cases via the proposed analytical technique and FEM. The results of both methods indicated excellent conformity. Furthermore, the effect of changes in thickness ratios of the layers was examined. Lastly, the cross-linking density of the hydrogel layer and some other parameters were studied to investigate their influence on the bilayer deformation and specify the optimal values of some of those parameters for the considered bilayers.