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The Flory&ndash, Rehner theoretical description of the free energy in a hydrogel swelling model can be broken into two swelling components: the mixing energy and the ionic energy. Conventionally for ionized gels, the ionic energy is characterized as the main contributor to swelling and, therefore, the mixing energy is assumed negligible. However, this assumption is made at the equilibrium state and ignores the dynamics of gel swelling. Here, the influence of the mixing energy on swelling ionized gels is quantified through numerical simulations on sodium polyacrylate using a Mixed Hybrid Finite Element Method. For univalent and divalent solutions, at initial porosities greater than 0.90, the contribution of the mixing energy is negligible. However, at initial porosities less than 0.90, the total swelling pressure is significantly influenced by the mixing energy. Therefore, both ionic and mixing energies are required for the modeling of sodium polyacrylate ionized gel swelling. The numerical model results are in good agreement with the analytical solution as well as experimental swelling tests.

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.

A hydrogel is a polymeric three-dimensional network structure. The applications of this material type are diversified over a broad range of fields. Their soft nature and similarity to natural tissue allows for their use in tissue engineering, medical devices, agriculture, and industrial health products. However, as the demand for such materials increases, the need to understand the material mechanics is paramount across all fields. As a result, many attempts to numerically model the swelling and drying of chemically responsive hydrogels have been published. Material characterization of the mechanical properties of a gel bead under osmotic loading is difficult. As a result, much of the literature has implemented variants of swelling theories. Therefore, this article focuses on reviewing the current literature and outlining the numerical models of swelling hydrogels as a result of exposure to chemical stimuli. Furthermore, the experimental techniques attempting to quantify bulk gel mechanics are summarized. Finally, an overview on the mechanisms governing the formation of geometric surface instabilities during transient swelling of soft materials is provided.