# Characterization of Hydrogel Deformation Using Two-Parameter Hyperelastic Models

## TL;DR

This paper compares different hyperelastic models to better understand how hydrogels deform under stress, finding that two-parameter models offer improved accuracy over traditional methods.

## Contribution

The study introduces the use of two-parameter hyperelastic models to more accurately characterize hydrogel deformation across a wide strain range.

## Key findings

- The Ogden model best fits stress–strain curves and reduced stress plots across various hydrogel formulations.
- The Localization and Rubinstein–Panyukov models capture low-strain behavior and maxima in Mooney plots above the overlap concentration.
- Entanglements significantly influence hydrogel deformation, with their effect diminishing at higher network concentrations.

## Abstract

Hyperelastic models for the deformation of hydrogels were evaluated as alternatives to the widely used neo-Hookean model. Poly(ethylene glycol diacrylate) (PEGDA) was synthesized via photopolymerization, with precursor molecular weights from 700 to 4000 Da and synthesis concentrations between 5 and 30 wt% in water. Hydrogels are often modeled as neo-Hookean solids; this model holds only over a limited strain range. To model deformation over a broader range and seek additional insight into gel network structures, the Mooney–Rivlin, Ogden, Rubinstein–Panyukov, and Localization models were applied to uniaxial compression data and their fits assessed against “Mooney plots” of reduced stress versus the inverse extension ratio. The Ogden model best fits the stress–strain curves to higher ratios and the reduced stress plots over the broadest range of formulations. The Localization and Rubinstein–Panyukov models fit well above c*, the overlap concentration, capturing low-strain behavior and the observed maxima under compression in Mooney plots. The Mooney–Rivlin model fit the stress–strain curves but was unable to fit the reduced stress plots. The Localization and Rubinstein–Panyukov model parameters suggest that entanglements play a significant role at all concentrations, with their contribution decreasing as the network concentration increases. This demonstrates the potential of using two-parameter models to understand the deformation of hydrogels.