Dehydration-induced entanglements (DIEs)Our strategy comprises two essential elements. The first key point involves maintaining a low degree of cross-linking, which results in the formation of a long-chain structure. During the polymerization of a hydrogel, monomers connect into chains, and those chains are cross-linked into a three-dimensional network. Simultaneously, interchain entanglements are formed (Fig. 2a). It is worth noting that long chains are more susceptible to entanglement compared to short chains. The entanglements formed during the polymerization process are labeled as polymerization-induced entanglements (PIEs). Certain PIEs cannot be removed, unless the chains are broken (Fig. 2a1). These inextricable entanglements are common in hydrogels prepared with a high polymer content14. Nevertheless, some PIEs can be removed through the application of external forces (Fig. 2a2). And there are also chains that remain unentangled (Fig. 2a3). The polymerization-induced entanglements are well understood with the development of polymer physics36,37,38.Fig. 2: Schematic diagram of entanglements in a hydrogel.a Polymerization-induced entanglements (PIEs) are formed in an as-prepared hydrogel: (a1) Some PIEs cannot be removed unless chain scission happens. (a2) Some PIEs can be removed by external forces. (a3) Some chains are not entangled. b Dehydration-induced entanglements (DIEs) are introduced during hydrogel dehydration: (b1-b2) Additional DIEs are introduced based on the existing PIEs. (b3) Some initially unentangled chains form DIEs. c The dehydrated hydrogel is stretched: (c1) The DIEs are disentangled but the PIEs are not removed. (c2) Both PIEs and DIEs are removed by external forces. (c3) The DIEs are removed by external forces.The second key point in our strategy centers on the dehydration-induced entanglements (DIEs), which, despite some recent research39,40, have not received full appreciation. When dehydrated, a hydrogel shrinks (Fig. 2b). The end-to-end distance of each single chain decreases, causing the chain to adopt a more curly conformation. In the meantime, the polymer chains get closer to each other. As a result, for the chains with PIEs already, additional DIEs are introduced (Fig. 2b1 and b2). And some originally unentangled chains form DIEs (Fig. 2b3)41. When the dehydrated hydrogel is stretched, all the DIEs are removable, but some PIEs cannot be removed (Fig. 2c). The PIEs demonstrated by Fig. 2a1 are not removed, and they work as topological cross-linkers (Fig. 2c1). Other PIEs and DIEs are disentangled by external force (Fig. 2c2 and c3).Entanglements-related hyperelasticity and stiffeningWe first demonstrate the influence of the degree of cross-linking and dehydration on hyperelasticity and modulus of hydrogels. We prepared hydrogels with three different degrees of cross-linking, and the initial water content was 87%. They are named high cross-linked (HC) hydrogels, medium cross-linked (MC) hydrogels, and low (loosely) cross-linked (LC) hydrogels, respectively. The as-prepared MC hydrogel with \({\phi }_{w0}\) = 87% is just the regular hydrogel mentioned in Fig. 1b. The as-prepared hydrogel samples were dehydrated/swelled to lower/higher water contents, and then stretched uniaxially by quasi-static loading. The corresponding quasi-static nominal stress-stretch ratio curves (s-s curves) for LC/MC/HC hydrogels with various water contents (\({\phi }_{w}\)) are exhibited in Fig. 3a-c, respectively.Fig. 3: Quasi-static nominal stress-stretch ratio curves and moduli.Uniaxially quasi-static nominal stress-stretch ratio curves (s-s curves) for a Low cross-linked (LC) hydrogels, b Medium cross-linked (MC) hydrogels, and c High cross-linked (HC) hydrogels with various water contents \({\phi }_{w}\). d Experimental results and theoretical predictions of elastic modulus (E) – polymer content (\({\phi }_{p}\)) relationships for LC/MC/HC hydrogels. Experimental data are presented as mean values +/- SD (n\(\ge\)3). e Theoretical cross-linked modulus (Ec) – polymer content (\({\phi }_{p}\)) relationships for LC/MC/HC hydrogels. f Theoretical entangled modulus (Ee) – polymer content (\({\phi }_{p}\)) relationships for LC/MC/HC hydrogels.For the LC hydrogels, as shown in Fig. 3a, the quasi-static s-s curve increases significantly when the hydrogel is dehydrated from \({\phi }_{w0}\) = 87% to \({\phi }_{w}\) = 40%. Furthermore, the phenomenon of strain-softening, characterized by a decrease in tangent modulus with an increasing stretch ratio, becomes more pronounced as dehydration increases. This strain-softening behavior is closely associated with interchain entanglements42,43,44. As the external load increases, the DIEs are removed gradually, leading to the continuous decrease of the tangent modulus of a s-s curve41. For certain LC hydrogels with relatively low \({\phi }_{w}\), the stress even drops when the stretch ratio increases. A lower \({\phi }_{w}\) corresponds to more DIEs, and their disentanglement under external loading results in a more pronounced strain-softening behavior. As a comparison, the MC/HC hydrogels show less strain-softening (Fig. 3b and c) when dehydrated to the same \({\phi }_{w}\) as the LC hydrogels, mainly due to the fact that the shorter chains are harder to form interchain entanglements. Further analyses will be given below.The DIEs contribute to the elastic modulus. A low degree of cross-linking is more conducive to stiffening the hydrogel by dehydration. Figure 3d shows the elastic modulus (E)-polymer content (\({\phi }_{p}\)) relationships for LC/MC/HC hydrogels in a log-log plot. The data points represent the experimental results, and the solid lines depict the theoretical predictions based on a constitutive model41. It is worth noting that the moduli shown in Fig. 3 were derived from the quasi-static s-s curves. Therefore, the moduli presented here do not include the contribution of viscoelasticity. The log(E)-log(\({\phi }_{p}\)) curve of LC hydrogels is much steeper than those of MC/HC hydrogels. For as-prepared hydrogels (\({\phi }_{w0}\) = 87%, i.e., \({\phi }_{p0}\) = 13%), the difference between their moduli is evident, and the higher the degree of cross-linking, the larger the modulus. When dehydrated to a water content of \({\phi }_{w}\) = 70%, these hydrogels exhibit similar moduli. However, with further dehydration, we found that the lower the degree of cross-linking, the larger the modulus. The modulus of a LC hydrogel increases rapidly as the water content decreases, which is beneficial to achieve stiffening by dehydration. For instance, the modulus of a LC hydrogel increases five folds, from 8.4 kPa to 50.9 kPa, when the water content drops from 87% to 70%. In contrast, the modulus of a HC hydrogel only increases by 0.76 times after the same dehydration process.The variation of E-\({\phi }_{p}\) curves with various cross-linking degrees shown in Fig. 3d was further analyzed in conjunction with a constitutive model. Theoretically, the modulus of a hydrogel consists of the contribution from the cross-linked networks (the cross-linked modulus, Ec) and the contribution from the interchain entanglements (the entangled modulus, Ee). When dehydrated, both Ec and Ee increase, satisfying corresponding scaling laws41. According to the polymer physics36, there is a critical polymer content, \({\phi }_{e}\), which corresponds to the boundary between unentangled and entangled regimes. The modulus of a hydrogel is dominated by Ec in the unentangled regime (\({\phi }_{p} \, < \, {\phi }_{e}\)), while dominated by Ee in the entangled regime (\({\phi }_{p} \, > \, {\phi }_{e}\))38. When \({\phi }_{p} \, > \, {\phi }_{e}\), the entangled modulus increases greatly with dehydration. The scaling laws between Ec, Ee, and \({\phi }_{p}\) are embedded into a hyperelasticity model (More details can be found in Supplementary Note 1).We compare this model with the quasi-static s-s curves presented in Fig. 3a-c (See Supplementary Fig. 1 and Supplementary Fig. 2). The fitted model parameters (See Supplementary Table 1) are adopted to predict the theoretical E-\({\phi }_{p}\) curves (Fig. 3d), Ec-\({\phi }_{p}\) curves (Fig. 3e), and Ee-\({\phi }_{p}\) curves (Fig. 3f). According to Fig. 3e, the log(Ec)-log(\({\phi }_{p}\)) curves for hydrogels with different degrees of cross-linking appear linear, exhibiting little difference in slope. By comparing Fig. 3d and Fig. 3f, we observed that the evolution of elastic modulus with \({\phi }_{p}\) is mainly dominated by the evolution law between Ee and \({\phi }_{p}\). The slopes of the log(\({E}_{e}\))-log(\({\phi }_{p}\)) curves for LC/MC/HC hydrogels do not differ significantly when \({\phi }_{p} \, > \, {\phi }_{e}\) (Fig. 3f). However, the critical polymer content of these hydrogels varies greatly. The HC hydrogels and MC hydrogels possess critical polymer contents of Ï•e = 31.1% and Ï•e = 18.0%, respectively, while the Ï•e of the LC hydrogels is expected to be less than 7% (See Supplementary Note 2 and Supplementary Fig. 1 for more detailed analysis). Accordingly, hydrogels with shorter chains are more difficult to form abundant entanglements by dehydration. Even when a HC hydrogel is dehydrated to Ï•w = 70%, substantial entanglements are not observed (the ratio of entangled modulus to cross-linked modulus is \({\alpha }_{{en}}\) = 0.61, indicating that the entangled modulus is smaller than the cross-linked modulus) due to the current polymer content (\({\phi }_{p}\) = 30%) still being below the critical polymer content (\({\phi }_{e}\) = 31.1%). On the contrary, quite a few entanglements exist in the as-prepared LC hydrogel, given that the critical polymer content (\({\phi }_{e}\) < 7%) is smaller than the initial polymer content (\({\phi }_{p0}\) = 13%). As a result, once dehydrated, the DIEs arise instantly, leading to a rapid increase in the entangled modulus.In addition, the contribution of entanglements to the elastic modulus rises vastly with progressive dehydration. As depicted in Fig. 3e and f, for LC/MC/HC hydrogels, The slopes of the log(\({E}_{e}\))-log(\({\phi }_{p}\)) curves (k = 2.93, 2.33, and 2.63, respectively) are much larger than those of the log(\({E}_{c}\))-log(\({\phi }_{p}\)) curves (k = 0.36, 0.56, and 0.46, respectively) when \({\phi }_{p}\) > \({\phi }_{e}\). For example, in the case of a LC hydrogel, the ratio of entangled modulus to cross-linked modulus (\({\alpha }_{{en}}\)) escalates fast from 4.5 to 38.9 as the water content reduces to 70%. Without the presence of substantial entanglements, the enhancement of stiffness with dehydration would be much slower.In conclusion, the stiffening of LC hydrogels by slight dehydration is quite efficient, thanks to the low critical polymer content of the long-chain structure and the sharp enhancement of entangled modulus by dehydration.Fracture toughness, crack-insensitivity, and energy dissipationA hydrogel with a conventional single network structure encounters stiffness (E)-fracture stretch (\({\lambda }_{f}\)) conflict. Consider a hydrogel with n polymer chains per unit volume and N monomers on each chain, the elastic modulus E is inversely proportional to the chain length N, while the fracture stretch \({\lambda }_{f}\) is proportional to \(\sqrt{N}\). If the chain length N decreases, the modulus increases, but the fracture stretch decreases. This E-\({\lambda }_{f}\) conflict is clearly demonstrated by the s-s curves of the as-prepared LC/MC/HC hydrogels in Fig. 4a. Taking the current strategy, a LC hydrogel was mildly dehydrated to \({\phi }_{w}\) = 70%, the resulting hydrogel resolves the E-\({\lambda }_{f}\) conflict. As shown in Fig. 4a, the s-s curves of the dehydrated LC hydrogel (black lines) completely encircle those of the as-prepared LC hydrogel (blue lines), indicating that the modulus, stretchability, strength, and work of fracture are simultaneously improved by mild dehydration. Besides, the slightly-dehydrated LC hydrogel (black lines) is stiffer than the as-prepared HC hydrogel (red lines), even though the density of the cross-linkers of the latter is 14 times that of the former.Fig. 4: Fracture and energy dissipation of hydrogels.a The s-s curves of the as-prepared LC/MC/HC hydrogels and slightly-dehydrated LC hydrogels (\({\phi }_{w}\) = 70%) by pure shear tests. The slightly-dehydrated LC hydrogel exhibits larger modulus, fracture stretch, strength, and work of fracture. b The fracture toughness of LC/MC/HC hydrogels with various \({\phi }_{w}\) values measured by pure shear tests. Data are presented as mean values +/− SD (n\(\ge\)3). c The fracture stretches for uncut samples (the plain bars) and precut samples (the patterned bars) of LC/MC/HC hydrogels with various \({\phi }_{w}\) values. Data are presented as mean values +/− SD (n\(\ge\)3). d The snapshots of a slightly-dehydrated LC hydrogel (\({\phi }_{w}\) = 70%) under various deformation. The crack does not grow at a stretch ratio of 20. e The s-s curve in a loading-unloading cycle at a strain rate of \(\dot{\varepsilon }\) = 0.1 s−1. The LC hydrogels show larger hysteresis loops. f The hysteresis ratios of LC/MC/HC hydrogels with various \({\phi }_{w}\) values measured by uniaxial tension tests. Data are presented as mean values +/− SD (n\(\ge\)3). g Four families of PAAm hydrogels are plotted on the toughness-modulus plane. The slightly-dehydrated LC hydrogels by the current strategy, with \({\phi }_{w}\) ranging from 65% to 87%, break the toughness-stiffness conflict, while the other strategies did not.We measured the fracture toughness of LC/MC/HC hydrogels with various water contents by pure shear tests. A sample with a width of 50 mm, a height of 10 mm, and a thickness of about 2 mm was stretched along the height direction, and the sample fractured at a stretch ratio of \({\lambda }_{f}\). Another specimen, with identical dimensions, was prefabricated with a 20 mm-long crack. This precut sample was stretched along the height direction, and the fracture stretch was labeled as \({\lambda }_{c}\). Then the fracture toughness values were calculated (See Methods and Supplementary Figs. 3–5) and presented in Fig. 4b. The results reveal that the fracture toughnesses of MC/HC hydrogels are greatly improved with dehydration. The toughness of the MC/HC hydrogels increases 5.9 times and 24.8 times, respectively, when the water content reduces from \({\phi }_{w0}\) = 87% to \({\phi }_{w}\) = 40%. However, the toughness of these hydrogels remains below 3000 J m−2. The LC hydrogels are also toughened when slightly dehydrated. A LC hydrogel with \({\phi }_{w}\) = 70% reaches a fracture toughness of 9782.5 J m−2. Such a high fracture toughness arises from the synergy of multiple mechanisms as will be enumerated below.First, this hydrogel is highly stretchable. As mentioned above, LC hydrogels possess longer polymer chains, leading to a larger fracture stretch. As evident in Fig. 4c, the fracture stretch of the as-prepared LC hydrogel is \({\lambda }_{f}\) = 17.9, while the slightly-dehydrated hydrogel (\({\phi }_{w}\) = 70%) is even more stretchable, with \({\lambda }_{f}\) = 20.6. The shrinkage of the hydrogel causes the polymer chains to curl up further, demanding additional deformation to reach their stretch limit. Consequently, the dehydrated hydrogel becomes more stretchable, contributing to its improved toughness.Second, a mildly-dehydrated LC hydrogel is quite crack-insensitive. As illustrated in Fig. 4d, a slightly-dehydrated LC hydrogel (\({\phi }_{w}\) = 70%) was prefabricated with a 20 mm-long crack. As the stretch increases, the crack gradually blunts without propagating, even if the stretch ratio reaches 20. The sample finally fails close to the clamp. Typically, a large crack greatly reduces the stretchability of a hydrogel, i.e., \({\lambda }_{c} \, \ll \, {\lambda }_{f}\) (As seen in the fracture stretches of MC/HC hydrogels in Fig. 4c). However, the fracture stretch of a precut LC hydrogel with \({\phi }_{w}\) = 70% is very close to that of an uncut sample (with \({\lambda }_{c}\) = 20.2 and \({\lambda }_{f}\) = 20.6, respectively. See Fig. 4c). And the precut LC hydrogel (\({\phi }_{w0}\) = 87%) can even stretch slightly further than the corresponding uncut hydrogel (with \({\lambda }_{c}\) = 19.2 and \({\lambda }_{f}\) = 17.9, respectively. See Fig. 4c), indicating a strong crack-insensitivity. The proximity between \({\lambda }_{c}\) and \({\lambda }_{f}\) for LC hydrogels with high water content is attributed to their large fractocohesive length. The fractocohesive length, Rf, defined as the ratio of the fracture toughness to the work of fracture, describes a material-specific length that marks the transition from flaw-insensitive to flaw-sensitive fracture45. To verify, larger samples of LC hydrogels with \({\phi }_{w}\) = 70% (a width of 120 mm, a height of 40 mm, a thickness of about 3 mm, and a 48 mm-long crack for precut samples) were tested. The results reveal smaller fracture stretches for precut hydrogels (with \({\lambda }_{c}\) = 17.8 and \({\lambda }_{f}\) = 22.1, respectively. See Supplementary Fig. 6). The precut samples fractured due to the propagation of the crack. The calculated fractocohesive length of LC hydrogels (\({\phi }_{w}\) = 70%) is determined to be 28.5 mm. This value exceeds the crack length of the small samples (20 mm) used in pure shear tests, aligning with the observed crack-insensitivity of small samples.The third mechanism underlying the ultra-large toughness is the combination of a large fracture process zone and a strong energy dissipation capacity. When the material surrounding the crack tip undergoes large deformation, the dehydration-induced entanglements are gradually removed. This disentanglement process, which involves the movement and friction of polymer chains, consumes a substantial amount of energy. It should be noted that the fractocohesive length also characterizes the size of the fracture process zone (FPZ). Though only a small fraction of chains in the FPZ break, all the energy dissipated in the FPZ contributes to the fracture toughness46. The fractocohesive length of a mildly-dehydrated LC hydrogel (28.5 mm) is much larger than that of MC/HC hydrogels (ranging from 0.3 to 2.5 mm. See Supplementary Fig. 7). Moreover, LC hydrogels possess a better capacity to dissipate energy. As shown in Fig. 4e, the as-prepared MC/HC hydrogels are highly elastic, with tiny hysteresis loops between loading and unloading curves. When they are dehydrated to a low water content of 40%, medium hysteresis loops are observed. In contrast, both the as-prepared LC hydrogel and the slightly-dehydrated LC hydrogel exhibit large hysteresis loops. The hysteresis ratio, defined as the area ratio between the hysteresis loop and the region under the loading curve, is listed in Fig. 4f. The slightly-dehydrated LC hydrogel (\({\phi }_{w}\) = 70%) demonstrates optimal energy dissipation capacity, with the dissipated energy accounting for approximately half of the work performed by the external force.A large FPZ around the crack tip dissipates energy substantially, so that the stress concentration at the crack tip is effectively alleviated, and the hydrogel is greatly toughened. The fractocohesive length of LC hydrogels with \({\phi }_{w}\) = 70% (Rf = 28.5 mm) lies between the height of small samples (H = 10.0 mm) and the height of large samples (H = 40 mm). The size of the FPZ for large samples (Rf = 28.5 mm) is much larger than that of the small samples (Rf = 10.0 mm). With more materials to dissipate energy, the measured toughness of the large samples is much higher, being \(\Gamma\)=21752 J m−2 (See Supplementary Fig. 6). We also tested the toughness of the as-prepared LC hydrogels using large samples (a width of 150 mm, a height of 40 mm, a thickness of about 3 mm, and a 60 mm-long crack for precut samples), the measured toughness is \(\Gamma\)=10152 J m−2 (See Supplementary Fig. 8), which is about 2.5 times larger than the toughness of small samples (\(\Gamma\) = 4109.6 J m−2). Obviously, the fracture toughness measured by pure shear tests is dependent on the sample size. Similar phenomena were observed in the measurement of toughness by the 90-degree peeling test46 and 180-degree peeling test47. The fractocohesive length is a critical size; below this size, the toughness increases with the sample size, while above it, the toughness reaches a plateau. We emphasize that in the comparison of fracture toughness values for different hydrogels tested in this paper, a fair comparison is ensured by considering the measured fracture toughness values for samples of identical dimensions (50 × 10 × 2 mm). For example, the fracture toughness of the LC hydrogel with \({\phi }_{w}\) = 70% is reported as \(\Gamma\) = 9782.5 J m−2 rather than \(\Gamma\) = 21752 J m-2 in Fig. 4b and g.The slightly-dehydrated LC hydrogels, with a relatively high content of water, resolve the stiffness-fracture toughness conflict. The LC hydrogels were prepared and then dehydrated to different water content: \({\phi }_{w}\) = 75%, 70%, and 65%, respectively. The moduli and fracture toughnesses of these hydrogels, along with some other PAAm hydrogels from references14,40, are listed in Fig. 4g. Regular PAAm hydrogels are either soft or brittle. Certain PAAm hydrogels with specific designs and processing have achieved higher toughness and modulus than regular PAAm hydrogels14,40. In contrast, adopting the current strategy, the fracture toughness of the LC hydrogel with \({\phi }_{w}\) = 70% approaches ten thousand J m-2. The LC hydrogel with \({\phi }_{w}\) = 65% reaches a high modulus (143.1 kPa) and a large toughness (9489.6 J m−2) simultaneously. The dense entanglements induced by dehydration not only stiffen but also toughen the hydrogel, breaking the stiffness-toughness conflict.Fatigue-resistanceWe tested the fatigue threshold \({\Gamma }_{0}\) of the slightly-dehydrated LC hydrogel (\({\phi }_{w}\) = 70%). As illustrated in Fig. 5a, precut samples were cyclically loaded with various maximal stretch ratios \({\lambda }_{m}\), and the crack growth processes were recorded. To calculate the corresponding energy release rates G, another uncut sample was also stretched cyclically. After 100 cycles with a maximal stretch ratio of \({\lambda }_{X}\), we upscaled the maximal stretch ratio to a larger value (Fig. 5b). The values of the maximal stretch ratio adopted here correspond to the values of \({\lambda }_{m}\) in fatigue tests. During the initial 10 cycles, the maximal stress in each cycle obviously attenuated, eventually stabilizing after 100 cycles (See Fig. 5c and Supplementary Fig. 9). In the 100th cycle of the cyclic experiments with a maximal stretch ratio of \({\lambda }_{m}\) = 2.65, a stable hysteresis loop was observed (Fig. 5d). A similar hysteresis loop was also observed in the 100th cycle of the cyclic experiments with \({\lambda }_{m}\) = 4.70. We believe that some entanglements are progressively removed with each cycle, leading to the gradual attenuation of the maximal stress (Fig. 5c). Some entanglements are reversible, as they are removed during loading and reformed during unloading, resulting in the stable hysteresis loop (Fig. 5d).Fig. 5: Fatigue-resistance of slightly-dehydrated LC hydrogels.a A precut slightly-dehydrated LC hydrogel (\({\phi }_{w}\) = 70%) is cyclically loaded with a maximal stretch ratio of \({\lambda }_{m}\), and the crack growth process is recorded. b An uncut sample is cyclically loaded with an increasing maximal stretch ratio to measure the corresponding energy release rates. c With \({\lambda }_{m}\) = 2.65, the maximal stress of each cycle decays to a stable value after 100 cycles. d Stable hysteresis loops are observed after 100 cycles with certain \({\lambda }_{m}\). e A precut sample is loaded with an energy release rate of 256.1 J m−2. The crack grows during the initial few thousand cycles and then is immobilized. f The crack growth process of precut samples under various energy release rates. g The relationship between crack extension per cycle (dc/dN) and the energy release rate (G). The calculated fatigue threshold is 291.4 J m−2.A precut LC hydrogel with \({\phi }_{w}\) = 70% was cyclically loaded with \({\lambda }_{m}\) = 2.65 (i.e., an energy release rate of 256.1 J m−2). As shown in Fig. 5e, after five thousand cycles, the crack propagated by about 1 mm. However, upon comparing snapshots taken in the 5000th and 20000th cycles, it was evident that the crack was then immobilized. When a larger \({\lambda }_{m}\) was applied (\({\lambda }_{m}\) = 3.90, i.e., energy release rate G = 425.3 J m−2), the crack grew fast during the initial few thousand cycles, followed by steady growth thereafter (Fig. 5f). The steady growth region was adopted to calculate the crack growth velocity. Figure 5g plots the relation between the crack extension per cycle (dc/dN) and the energy release rate G. The fatigue threshold was determined to be 291.4 J m−2, a large value considering that conventional PAAm hydrogels and natural rubber typically have fatigue thresholds of around ~10 J m−2 and ~50 J m−2, respectively.The low degree of cross-linking facilitates long polymer chains, which endow the LC hydrogels with a high fatigue threshold. A fatigue crack grows by breaking only a single layer of deformed chains across the crack plane. According to the Lake-Thomas model18, the fatigue threshold is equivalent to the energy stored in a layer of polymer chains per unit area19,48: \({\Gamma }_{0}\) = \({\phi }_{p}^{2/3}l\sqrt{N}J/V\), where \({\phi }_{p}\) represents the polymer content of a hydrogel, l is the length of a monomer, N is the number of monomers in a single chain, J is the chemical bond energy, and V is the volume of a monomer. Obviously, the longer the polymer chains (i.e., larger N), the larger the \({\Gamma }_{0}\). Thus, a long-chain structure serves as the basis for fatigue-resistant hydrogels. However, simply increasing the chain length does not lead to a significant improvement in the fatigue threshold. In our work, the chain length of the as-prepared LC hydrogels is 30 times that of the as-prepared HC hydrogels, which means the enhancement of the threshold is less than 6 times (\({\Gamma }_{0}\) ~ \(\sqrt{N}\)). Since the fatigue crack breaks a layer of chains across the crack plane, increasing the chain density (i.e., the polymer content) can raise the threshold. Dehydration of a hydrogel enlarges the chain density, thereby further contributing to the fatigue threshold. Studies have shown that the classical Lake-Thomas model agrees well with measured \({\Gamma }_{0}\) of hydrogels with high water content, but it underestimates the \({\Gamma }_{0}\) when the water content decreases48. Recent research demonstrated that the threshold of a dehydrated hydrogel follows the scaling law49: \({\Gamma }_{0}({\phi }_{p}) \sim {\phi }_{p}^{3\nu /(3\nu -1)}\), where \(\nu\) is the same scaling exponent as adopted in the Gc-\({\phi }_{p}\) and Ge-\({\phi }_{p}\) relationships (See Eqs. 4 and 5 in Supplementary Note 1). Interestingly, the scaling law for \({\Gamma }_{0}\) is similar to the scaling law for Ge when \({\phi }_{p}\) > \({\phi }_{e}\) (Eq. 5 in Supplementary Note 1). As discussed above, the modified scaling law between the threshold and chain length and current polymer content is as follows: \({\Gamma }_{0}({\phi }_{p}) \sim \sqrt{N}{\phi }_{p}^{3\nu /(3\nu -1)}\). The scaling exponent for LC hydrogels is \(\nu\) = 0.506 (Supplementary Table 1). According to the modified scaling law, compared with the regular hydrogel, the fatigue threshold of the dehydrated LC hydrogel (\({\phi }_{w}\) = 70%) can be increased by 36.7 times, which is comparable with the observed 27-fold improvement by experiment. It is evident that the combination of a long-chain structure and dehydration-induced increment of chain density significantly improves the fatigue threshold.Overall mechanical propertiesThe current strategy fabricated hydrogels with excellent overall mechanical properties. The mechanical properties of four PAAm hydrogels were compared: hydrogel A with a water content of \({\phi }_{w0}\) = 70%, hydrogel B with a water content of \({\phi }_{w0}\) = 87%, hydrogel C prepared by the current strategy, with an initial water content of \({\phi }_{w0}\) = 87% and a current water content of \({\phi }_{w}\) = 70%, and a regular hydrogel with medium cross-linking and \({\phi }_{w0}\) = 87% (i.e., the regular hydrogel shown in Fig. 1b). Hydrogel A, B, and C were prepared with low cross-linking (Supplementary Fig. 10a). Hydrogel C was dehydrated from hydrogel B. By slight dehydration, the overall mechanical properties, including the modulus, fracture stretch, strength, work of fracture, fracture toughness, and fatigue threshold, are simultaneously improved (See Fig. 4a and Supplementary Table 2). In comparison with the regular hydrogel, the fracture toughness, fatigue threshold, and modulus of hydrogel C increased by 25.0 times, 27.0 times, and 3.9 times, respectively. Obviously, the current strategy breaks the toughness-stiffness and fatigue threshold-stiffness conflicts. Moreover, the enhancement of the fatigue threshold is comparable with the increase in toughness. From another perspective, hydrogel A and hydrogel C share identical chemical components, i.e., the current water content of \({\phi }_{w}\) = 70%, a cross-linker-to-monomer molar ratio of 5.0 × 10-5, and an initiator-to-monomer molar ratio of 1.0×10-3. However, the processing and microstructure are quite different. Owing to the lower initial polymer content of hydrogel C, its modulus is slightly smaller than that of hydrogel A, measuring at 83% of the modulus of hydrogel A, and this aligns with the theory of polymer physics36. Nevertheless, hydrogel C is much tougher, with a fracture toughness of 21.8 times that of hydrogel A. In addition, its fatigue threshold is 4.1 times that of hydrogel A.As a demonstration, these four hydrogels were fabricated to lift a weight. Each hydrogel sample, with a width of 50 mm, a height of 10 mm, and a thickness of about 2 mm, was precut with a 20 mm-long crack and then stretched to lift a weight. The force-displacement curves are depicted in Supplementary Fig. 10b. In Supplementary Movie 1, it is evident that the crack does not propagate in hydrogel B due to its large toughness. However, hydrogel B fails to lift a 300 g weight as it is soft and weak, ultimately fracturing near the fixture (Supplementary Fig. 10c). Supplementary Movie 2 reveals that hydrogel A is also unable to lift a 300 g weight. Despite its higher modulus compared to hydrogel B, hydrogel A is too brittle, resulting in crack propagation (Supplementary Fig. 10d). The regular hydrogel performs even worse (see Supplementary Movie 3 and Supplementary Fig. 10b). By contrast, hydrogel C successfully lifts a 500 g weight (see Supplementary Movie 4 and Supplementary Fig. 10e), indicating that the hydrogel designed by the current strategy is both tough and strong.
