Fig. 4. Nonlinear rheology of granular hydrogels is modulated by the properties of the constituent microgels.

(A) Yielding transition of granular hydrogels (Ø = 55 μm building blocks) depicted in strain amplitude sweep measurements (γ = 0.1 to 100%, ω = 10 rad s⁻¹, 25°C) at different polymer contents. (B) Critical strain, γ_c, was measured as the strain at the crossover of G′ and G″ and showed a gradual decrease as a function of polymer content for Ø = 55 μm (blue) and Ø = 100 μm (red) building blocks (P < 0.001). (C) γ_c depended on the size of the building blocks for E = 120 kPa (dark blue; P < 0.05) and remained constant for E = 20 kPa (light blue; ns). (D) Loss moduli of granular hydrogels were normalized by their linear response value at low shear strain to calculate the energy dissipation during yielding. The overshoot in loss moduli, G″/G″_γ→0, was fitted to a log-normal distribution. The energy dissipated per unit volume was calculated by integrating the area under the curves of the loss moduli overshoot. Overlaid curves of the fitted G″/G″_γ→0, which shifted to higher shear strain values as microgel polymer content decreased. (E) Dissipated energies, E_d, increased as the stiffness of the microgel building blocks decreased, as shown for Ø = 55 μm (blue) and Ø = 100 μm (red) microgels (P < 0.001). (C) Fitted G″/G″_γ→0 curves of granular hydrogels of varying building block sizes. (F) E_d values both for soft (E = 20 kPa, light blue) and stiff (E = 120 kPa, dark blue) did not vary appreciably as a function of microgel size (ns). (B, C, E, and F) Plots are represented as means ± SEM, n = 3. Statistical analysis was performed using one-way ANOVA with Tukey’s test for post hoc analysis.