Radial Inhomogeneous Deformation and Twist-Extension Coupling in Hydrogel Cylinders Under Chemo-Mechanical Stimuli

Hydrogels, characterized by a factorial microscopic structure, generally exhibit homogeneous deformation under mechanical and chemical loads in the absence of directional reinforcement. However, curvilinear geometries, such as cylindrical specimens, may exhibit inhomogeneous deformation under torsion. This article explores the intriguing phenomenon where a hydrogel cylinder undergoes radial inhomogeneous deformation, accompanied by axial elongation during twisting. The study begins by presenting a thermodynamic framework that captures the chemo-mechanical interactions, encompassing the governing and constitutive equations. The free energy density is then specified for the hydrogel, followed by a Legendre transformation to incorporate the incompressibility condition with a new form of free energy density. After a detailed geometric analysis, we identify the factors that trigger inhomogeneity. Finally, an equilibrium analysis elucidates the effects of key parameters on the coupled twist-extension and radial inhomogeneous deformation of a hydrogel cylinder under torsion.