Combined extension and torsion of hydrogels with chemo-mechanical coupling: Revealing positive poynting effect

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory-Huggins parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel at equilibrium state is discussed, reaching some fundamental conclusions. Negative axial forces are captured, revealing the typical positive Poynting effect where the cylinder tends to elongate on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent.