Second-order elasticity of polymeric hydrogels with chemically coupled effects

In this paper, a second-order elastic model is formulated for polymeric hydrogels subject to chemo-mechanical coupled field. A third-order phenomenological free energy density is theoretically formulated based on the classical Flory-Huggins solution theory, and a fully coupled chemo-mechanical expression is obtained for the Lamé constants and second-order elastic constants, where the chemical influences are considered. The chemically induced swelling is analytically investigated for characterization of the chemically coupled elastic constants, where the relationship is revealed among the elastic constants, the swelling ratio, and the chemical potential. The effects of Flory parameter and degree of cross-linking are then theoretically analyzed on the elastic constants. Application of the present model to simple tension reveals the classical relation among the Lamé constants, Young's modulus and Poisson's ratio, where all the constants are dependent on the chemical potential. In addition, a stiffening effect is observed for the effect of second-order elastic parameters, where good agreement is presented with experimental data (Urayama et al., 2006). This model presents a theoretical platform to simulate the responsive behavior of polymeric hydrogels subject to chemo-mechanical coupled stimuli. The resultant elastic constants couple the chemical and mechanical effects, and may provide a comprehensive guide to structure analysis and design of soft materials.