Finite Deformation of Swollen pH-Sensitive Hydrogel Cylinder Under Extension and Torsion and its Poynting Effect: Analytical Solution and Numerical Verification

Abstract

According to the rise of technological interest in hydrogels, there is a growing necessity for precise mechanical and thermodynamic experimental characterizations. One of the common experimental protocols is applying combined extension-torsion loading on a cylinder. Therefore, we have proposed an analytical solution for the problem of torsion superimposed extension coupling with pH variation on a cylinder composed of the pH-sensitive hydrogel. Additionally, the Poynting effect as an inherently nonlinear phenomenon is studied for a hydrogel cylinder under extension-torsion loading. The finite deformation of a swollen cylinder is investigated using a constitutive model that captures network stretching, mixing of polymeric network and solvent, mixing of mobile ions with the solvent, and acidic groups’ dissociation. To evaluate the analytical solution accuracy, 3D finite element analysis (FEA) has been carried out for the same problem. In this regard, it is required to develop a user-defined subroutine, UHYPER, for pH-sensitive hydrogels; the developed subroutine is validated via free-swelling and constrained swelling problems. Compared to the FEA, the presented analytical solution is more interesting regarding its low computational cost. It is perceived that the computational cost of the analytic solution is much lower than the one required for FE analysis (around 1%). Thus, the proposed solution can be utilized as aneffective toolto examine each factor on the swelling behavior of hydrogels, including mechanical properties as well as loading parameters. Moreover, the developed analytical solution can be employed for calibrating material parameters. Finally, Poynting effects are examined for various axial stretches and twists, pH values, and cross-linked densities.