A viscoelastic constitutive law for hydrogels

Abstract

A viscoelastic constitutive law is developed for a hydrogel to encompass deviatoric deformations where the viscosity of the solvent contributes to the deviatoric stress of the system. The law is obtained in Kelvin–Voigt form by adding together the stress in the polymer network, the osmotic and solvent pressures and the viscous stress induced in the solvent. Transient behavior of the hydrogel is presented in terms of an example where transport of the solvent through the gel and viscosity due to deviatoric deformation interact to enable response that would otherwise be precluded, showing the significance of including the deviatoric viscosity. In addition, a simple relaxation problem is solved for a swollen hydrogel where volume of the hydrogel is preserved, namely small strain shear as induced in a rheometer.