In materials of all types, hysteresis and toughness are usually correlated. For example, a highly stretchable elastomer or hydrogel of a single polymer network has low hysteresis and low toughness. The single network is commonly toughened by introducing sacrificial bonds, but breaking and possibly reforming the sacrificial bonds causes pronounced hysteresis. In this paper, we describe a principle of stretchable materials that disrupt the toughness-hysteresis correlation, achieving both high toughness and low hysteresis. We demonstrate the principle by fabricating a composite of two constituents: a matrix of low elastic modulus, and fibers of high elastic modulus, with strong adhesion between the matrix and the fibers, but with no sacrificial bonds. Both constituents have low hysteresis (5%) and low toughness (300 J/m 2 ), whereas the composite retains the low hysteresis but achieves high toughness (10,000 J/m 2 ). Both constituents are prone to fatigue fracture, whereas the composite is highly fatigue resistant. We conduct experiment and computation to ascertain that the large modulus contrast alleviates stress concentration at the crack front, and that strong adhesion binds the fibers and the matrix and suppresses sliding between them. Stretchable materials of high toughness and low hysteresis provide opportunities to the creation of high-cycle and low-dissipation soft robots and soft human-machine interfaces. elastomer | stretchable materials | toughness | hysteresis | fatigue S tretchable materials such as elastomers and gels enable the fast-moving field of soft (and possibly biocompatible) systems. Examples include stretchable electronics (1-4), soft robots (5, 6), ionotronics (7-9), drug delivery (10, 11), and tissue regeneration (12). Many systems require that the stretchable materials have high toughness (i.e., dissipate much energy to resist the extension of cracks), but have low hysteresis (i.e., dissipate little energy during normal operation of load and unload). These two requirements, however, usually conflict: Toughness and hysteresis are often correlated. Toughness and hysteresis both result from energy dissipation, just under different conditions. A stretchable material of a single polymer network usually has low hysteresis and low toughness-that is, the stress-stretch curves for load and unload almost coincide, and the material ruptures at a much-reduced stretch when containing a crack (13).The toughness-hysteresis correlation has a molecular origin (Fig. 1A). A stretchable material such as an elastomer or a gel has a molecular architecture that mixes strong and weak bonds, enabling the hybrid behavior of solid and liquid. Strong bonds (e.g., covalent bonds) link monomer units into polymer chains, and cross-link the polymer chains into a network. Weak bonds (e.g., hydrogen bonds and van der Waals interaction) aggregate the monomer units of different polymer chains, as well as solvent molecules, into a condensed phase, but allow them to change neighbors constantly, transmit force negligibly, and ac...

Elastomers and gels can often deform multiple times their original length. The stretchability is insensitive to small cuts in the samples, but reduces markedly when the cuts are large. We show that this transition occurs when the depth of cut exceeds a material-specific length, defined by the ratio of the fracture energy measured in the large-cut limit and the work to rupture measured in the small-cut limit. This conclusion generalizes a result in the fracture mechanics of hard materials. For an acrylic elastomer and a polyurethane, we measure the stretch to rupture as a function of the depth of cut, and show that the experimental data agree well with the prediction of the nonlinear elastic fracture mechanics. In a space of material properties we compare many materials (elastomers, gels, ceramics, glassy polymers, biomaterials, and metals), and find that the material-specific length varies from nanometers to centimeters.

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Many living tissues achieve functions through architected constituents with strong adhesion. An Achilles tendon, for example, transmits force, elastically and repeatedly, from a muscle to a bone through staggered alignment of stiff collagen fibrils in a soft proteoglycan matrix. The collagen fibrils align orderly and adhere to the proteoglycan strongly. However, synthesizing architected materials with strong adhesion has been challenging. Here we fabricate architected polymer networks by sequential polymerization and photolithography, and attain adherent interface by topological entanglement. We fabricate tendon-inspired hydrogels by embedding hard blocks in topological entanglement with a soft matrix. The staggered architecture and strong adhesion enable high elastic limit strain and high toughness simultaneously. This combination of attributes is commonly desired in applications, but rarely achieved in synthetic materials. We further demonstrate architected polymer networks of various geometric patterns and material combinations to show the potential for expanding the space of material properties.