Analytical and Numerical Study of the Swelling Behavior in Functionally Graded Temperature-sensitive Hydrogel Shell

Abstract

In this article, analytical and numerical methods were employed to study swelling behavior of a cylindrical shell made of a functionally graded temperature sensitive hydrogel. The hydrogel shell has gradient property in radial direction. The shell cross-linking density is a linear function of the radial coordinate of the FGM shell. The analytical model was first developed for the hydrogel shell and a second order differential equation was derived which can be solved by numerical methods. Then, finite element solution of the under-study functionally graded hydrogel shell was performed by implementing the material model in ABAQUS software and by writing a user-defined subroutine. In this regard, the functionally graded hydrogel shell was modeled as multi-layered shell with discrete material properties. A good agreement between the analytical results and numerical simulation was observed and validity of analytical solution was confirmed. Thereafter, analytical model was employed to study the swelling behavior of functionally graded shell for different thickness ratios of the shell.