Coupled thermo-mechanical swelling of a thermo-responsive hydrogel hollow cylinder under extension-torsion: Analytical Solution and FEM

Abstract

In this article, the mechanical swelling behavior of poly-(N-isopropylacrylamide) hydrogel is scrutinized considering a hollow circular cylinder subjected to temperature variation-extension-torsion. Accordingly, an analytical solution is presented to consider the general combined loading on temperature-sensitive hydrogel cylinder for two approaches, considering same temperature for whole structure and solving heat equation to compute internal temperature of structure. Additionally, to evaluate the proposed solution, finite element analysis has been conducted for same problem which revealed excellent conformity for various case studies. Therefore, a user-material subroutine, UHYPER, is implemented to be employed in finite element analysis in order to define swelling of PNIPAM hydrogels. This subroutine was validated using free swelling and constraint swelling with previous and their analytical solutions. Regarding the complexity of material and loading namely, nonlinear finite behavior of hydrogel as well as combined cooling-extension-torsional loading, various factors, cross-linked density, axial stretch, torsional twist and temperature variation, were investigated to clarify the swelling behavior of hydrogel. Solving heat equation, in the second approach, enables us to apply various thermal conditions on this structure, while in previous studies, the temperature of whole structure is considered to vary simultaneously with the same function. This approach can help researchers to examine diverse thermo-mechanicals problem for temperature-sensitive hydrogels.