A strain induced softening and hardening constitutive model for superabsorbent polymers undergoing finite deformation

Abstract

Hydrogels have a wide range of applications from medical devices to tissue engineering to industrial health products. The numerical modeling of these porous structures can provide insight into their in-situ performance. However, an accurate constitutive model to replicate the stress-strain behavior of the swelling process is essential in ensuring the efficacy of the simulation. This study presents a strain dependent constitutive model for describing the finite deformation of superabsorbent polymers undergoing solvent induced swelling. Like many elastic materials, stretch-induced softening and hardening of these polymers occurs at large deformations. In order to incorporate the deformation dependent modulus into the new model, the shear modulus of sodium polyacrylate gels were measured using a rheometer as a function of swelling. Through numerical simulations on spherical gels, the effect of both cross-link density and the dependent modulus is investigated against a control model. As experimental quantification of the initial porosity is difficult and often not consistent between samples, Monte-Carlo simulations are implemented to experimentally verify the new model. Furthermore, this model is applied to experimental uniaxial tension data of incompressible rubber to allow comparison to other strain hardening constitutive models.