Effective mechanical properties of frozen hydrogel with ice inclusions

Hydrogel exhibits attractive mechanical properties that can be regulated to be extremely tough, strong and resilient, adhesive and fatigue-resistant, thus enabling diverse applications ranging from tissue engineering scaffolds, flexible devices, to soft machines. As a liquid-filled porous material composed of polymer networks and water, the hydrogel freezes at subzero temperatures into a new material composed of polymer matrix and ice inclusions: the frozen hydrogel displays dramatically altered mechanical properties, which can significantly affect its safety and reliability in practical applications. In this study, based upon the theory of homogenization, we predicted the effective mechanical properties (e.g., Young's modulus, shear modulus, bulk modulus and Poisson ratio) of a frozen hydrogel with periodically distributed longitudinal ice inclusions. We firstly estimated its longitudinal Young's modulus, longitudinal Poisson ratio and plane strain bulk modulus using the self-consistent method, and then its longitudinal and transverse shear modulus using the generalized self-consistent method; further, the results were employed to calculate its transverse Young's modulus and transverse Poisson ratio. We validated the theoretical predictions against both finite element (FE) simulation and experimental measurement results, with good agreement achieved. We found that the estimated transverse Poisson ratio ranges from 0.3 to 0.53 and, at low volume fraction of ice inclusions, exhibits a value larger than 0.5 that exceeds the Poisson ratios of both the polymer matrix and the ice inclusion (typically 0.33-0.35). Compared with other homogenization methods (e.g., the rule of mixtures, the Halpin-Tsai equations, and the Mori-Tanaka method), the present approach is more accurate in predicting the effective mechanical properties (in particular, the transverse Poisson ratio) of frozen hydrogel. Our study provides theoretical support for the practical applications of frozen liquid-saturated porous materials such as hydrogel.