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Hybrid double-network hydrogels are a class of material that comprise transiently and permanently crosslinked polymer networks and exhibit an enhanced toughness that is believed to be governed by the yielding of the transient polymer network. The precise role of the two polymer networks in this yielding transition and their interplay remains an open question that we address here through constructing a series of hydrogel designs in which the interaction within and between the two polymer networks are systematically inhibited or enhanced. We characterise each of the hydrogel designs using large amplitude oscillatory shear rheology (LAOS). Inspecting yielding through elastic stress across hydrogel designs, we elucidate that the hybrid double-network hydrogel exhibits a two-step yielding behaviour that originates from to the presence of transient crosslinks. Examining the rheological response within each oscillatory cycle and across the hydrogel designs, we show that the micro-structural changes in the transient network are crucial in the second stage of this yielding. We surmise that the first step of yielding is determined by the intermolecular interactions between the two polymer networks by systematically altering the strength of the interactions. These interactions also influence the second step of yielding, which we show is governed by the transient intermolecular interactions within the polymer networks. Our study therefore reveals that the interactions between the polymer networks are as crucial as within the polymer networks and therefore provides insights into how the yielding mechanisms in soft composite materials can be identified, adjusted, and controlled.

Folded protein hydrogels are prime candidates as tuneable biomaterials but it is unclear to what extent their mechanical properties have mesoscopic, as opposed to molecular origins. To address this, we probe hydrogels of the muscle-derived protein $I27_5$, using a multimodal rheology approach. Across multiple protocols, the hydrogels consistently exhibit power-law viscoelasticity in the linear viscoelastic regime with an exponent $\beta = 0.03$, suggesting a dense fractal meso-structure, with predicted fractal dimension $d_f = 2.48$. In the nonlinear viscoelastic regime, the hydrogel undergoes stiffening and energy dissipation, indicating simultaneous alignment and unfolding of the folded proteins. Remarkably, this behaviour is highly reversible, as the value of $\beta$, $d_f$ and the viscoelastic moduli return to their equilibrium value, even after multiple cycles of deformation. This highlights a previously unrevealed diversity of viscoelastic properties that originate on the mesoscopic scale. These considerations are likely to be key to controlling the viscoelasticity of folded protein hydrogels.

Intermediate filaments are cytoskeletal proteins that are key regulators of cell mechanics, a role which is intrinsically tied to their hierarchical structure and their unique ability to accommodate large axial strains. However, how the single-filament response to applied strains translates to networks remains unclear, particularly with regards to the crosslinking role played by the filaments' disordered "tail" domains. Here we test the role of these noncovalent crosslinks in the nonlinear rheology of reconstituted networks of the intermediate filament protein vimentin, probing their stress- and rate- dependent mechanics. Similarly to previous studies we observe elastic stress-stiffening but unlike previous work we identify a characteristic yield stress $\sigma^*$, above which the networks exhibit rate-dependent softening of the network, referred to as $\textit{inelastic fluidization}$. By investigating networks formed from tail-truncated vimentin, in which noncovalent crosslinking is suppressed, and glutaraldehyde-treated vimentin, in which crosslinking is made permanent, we show that rate-dependent inelastic fluidization is a direct consequence of vimentin's transient crosslinking. Surprisingly, although the tail-tail crosslinks are individually weak, the effective timescale for stress relaxation of the network exceeds 1000s at $\sigma^*$. Vimentin networks can therefore maintain their integrity over a large range of strains (up to ~1000\%) and loading rates (10$^{-3}$ to 10$^{3}s^{-1}$). Our results provide insight into how the hierarchical structure of vimentin networks contributes to the cell's ability to be deformable yet strong.

The cells and tissues that make up our body juggle contradictory mechanical demands. It is crucial for their survival to be able to withstand large mechanical loads, but it is equally crucial for them to produce forces and actively change shape during biological processes such as tissue growth and repair. The mechanics of cell and tissues is determined by scaffolds of protein polymers known as the cytoskeleton and the extracellular matrix, respectively. Experiments on model systems reconstituted from purified components combined with polymer physics concepts have already successfully uncovered some of the mechanisms that underlie the paradoxical mechanics of living matter. Initial work focussed on explaining universal features such as the nonlinear elasticity of cells and tissues in terms of polymer network models. However, living matter exhibits many advanced mechanical functionalities that are not captured by these coarse-grained theories. In this Review, we focus on recent experimental and theoretical insights revealing how their porous structure, structural hierarchy, transient crosslinking, and mechanochemical activity confer resilience combined with the ability to adapt and self-heal. These physical insights improve our understanding of cell and tissue biology and also provide a source of inspiration for synthetic life-like materials.