Granular hydrogels as brittle yield stress fluids.

While granular hydrogels are increasingly used in biomedical applications, methods to capture their rheological behavior generally consider shear-thinning and self-healing properties or produce ensemble metrics such as the dynamic moduli. Analytical approaches paired with common oscillatory shear tests can describe not only solid-like and fluid-like behavior of granular hydrogels but also transient characteristics inherent in yielding and unyielding processes. Combining oscillatory shear testing with consideration of Brittility (Bt) via the Kamani-Donley-Rogers (KDR) model, we show granular hydrogels behave as brittle yield stress fluids with complex transient rheology. We quantify steady and transient rheology as a function of microgel (composition; diameter) and granular (packing; droplet heterogeneity) assembly properties for mixtures of polyethylene glycol and gelatin microgels. The KDR model with Bt captures granular hydrogel behavior for a wide range of design parameters, reducing the complex transient rheology to a determination of model parameters. We describe the impact of composition on rheological behavior and model parameters in monolithic and mixed granular hydrogels. The model robustly captures self-healing behavior and reveals granular relaxation time depends on strain amplitude. This quantitative framework is an important step toward rational design of granular hydrogels for applications ranging from injection and in situ stabilization to 3D bioprinting.