Nonlinear elasticity of temperature-sensitive hydrogels with phase separation

In this work, a fully coupled second-order nonlinear elastic framework is established via perturbation analysis. This addresses the predictive limitations of current hydrogel models caused by undefined micro-macro correlations and inaccurate phase transition characterizations. A thermo-dependent Flory interaction parameter is incorporated, and closed-form elastic coefficients varying with temperature and chemical potential are derived. A double well free energy landscape is captured to characterize swelling-collapse phase transitions, whose critical conditions are identified through parametric analysis. Thermal modulation of elastic modulus and nonlinear mechanical responses is validated via uniaxial tension simulation and experimental data of poly-(N-isopropylacrylamide) hydrogels. With only five interpretable elastic parameters, the developed framework provides an efficient and reliable tool for multi-field mechanical analysis of responsive hydrogel materials.