Fracture toughness of hydrogels: measurement and interpretation

Flexible Artificial Tactility with Excellent Robustness and Temperature Tolerance Based on Organohydrogel Sensor Array for Robot Motion Detection and Object Shape Recognition

Hydrogel-based flexible artificial tactility is equipped to intelligent robots to mimic human mechanosensory perception. However, it remains a great challenge for hydrogel sensors to maintain flexibility and sensory performances during cyclic loadings at high or low temperatures due to water loss or freezing. Here, a flexible robot tactility is developed with high robustness based on organohydrogel sensor arrays with negligent hysteresis and temperature tolerance. Conductive polyaniline chains are interpenetrated through a poly(acrylamide-co-acrylic acid) network with glycerin/water mixture with interchain electrostatic interactions and hydrogen bonds, yielding a high dissipated energy of 1.58 MJ m-3, and ultralow hysteresis during 1000 cyclic loadings. Moreover, the binary solvent provides the gels with outstanding tolerance from -100 to 60 °C and the organohydrogel sensors remain flexible, fatigue resistant, conductive (0.27 S m-1), highly strain sensitive (GF of 3.88) and pressure sensitive (35.8 MPa-1). The organohydrogel sensor arrays are equipped on manipulator finger dorsa and pads to simultaneously monitor the finger motions and detect the pressure distribution exerted by grasped objects. A machine learning model is used to train the system to recognize the shape of grasped objects with 100% accuracy. The flexible robot tactility based on organohydrogels is promising for novel intelligent robots.

Dehydration drives damage in the freezing of brittle hydrogels

It is widely known that freezing breaks soft, wet materials. However, the mechanism underlying this damage is still not clear. To understand this process, we freeze model, brittle hydrogel samples, while observing the growth of ice-filled cracks that break these apart. We show that damage is not caused by the expansion of water upon freezing or the growth of ice-filled cavities in the hydrogel that exert pressure on the surrounding material. Instead, local ice growth dehydrates the adjacent hydrogel, leading to drying-induced fracture. This dehydration is driven by the process of cryosuction, whereby undercooled ice sucks nearby water toward itself, feeding ice growth. Our results highlight the strong analogy between freezing damage and desiccation cracking, which we anticipate being useful for developing an understanding of both topics. Our results should also give useful insights into a wide range of freezing processes, including cryopreservation, food science, and frost heave.

Curving expectations: The minimal impact of structural curvature in biological puncture mechanics

Living organisms have evolved various biological puncture tools, such as fangs, stingers, and claws, for prey capture, defense, and other critical biological functions. These tools exhibit diverse morphologies, including a wide range of structural curvatures, from straight cactus spines to crescent-shaped talons found in raptors. While the influence of such curvature on the strength of the tool has been explored, its biomechanical role in puncture performance remains untested. Here, we investigate the effect of curvature on puncture mechanics by integrating experiments with finite element simulations. Our findings reveal that within a wide biologically relevant range, structural curvature has a minimal impact on key metrics of damage initiation or the energies required for deep penetration in isotropic and homogeneous target materials. This unexpected result improves our understanding of the biomechanical pressures driving the morphological diversity of curved puncture tools and provides fundamental insights into the crucial roles of curvature in the biomechanical functions of living puncture systems.

Toughening Self-Healing Elastomers with Chain Mobility

Enhancing fracture toughness and self-healing within soft elastomers is crucial to prolonging the operational lifetimes of soft devices. Herein, it is revealed that tuning the polymer chain mobilities of carboxylated-functionalized polyurethane through incorporating plasticizers or thermal treatment can enhance these properties. Self-healing is promoted as polymer chains gain greater mobility toward the broken interface to reassociate their bonds. Raising the temperature from 80 to 120 °C, the recovered work of fracture is increased from 2.86 to 123.7 MJ m-3. Improved fracture toughness is realized through two effects. First, strong carboxyl hydrogen bonds dissipate large energies when broken. Second, chain mobilities enable the redistribution of localized stress concentrations to allow crack blunting, enlarging the size of dissipation zones. At optimal conditions of plasticizers (3 wt.%) or temperature (40 °C) to promote chain mobilities, fracture toughness improves from 16.3 to 19.9 and 25.6 kJ m-2, respectively. Insights of fracture properties at healed soft interfaces are revealed through double cantilever beam tests. These measurements indicate that fracture mechanics play a critical role in delaying complete failure at partial self-healing. By imparting optimal polymer chain mobilities within tough and self-healing elastomers, effective prevention against damage and better recovery are realized.

Unique stick-slip crack dynamics of double-network hydrogels under pure-shear loading

In this work, we have found that a prenotched double-network (DN) hydrogel, when subjected to tensile loading in a pure-shear geometry, exhibits intriguing stick-slip crack dynamics. These dynamics synchronize with the oscillation of the damage (yielding) zone at the crack tip. Through manipulation of the loading rate and the predamage level of the brittle network in DN gels, we have clarified that this phenomenon stems from the significant amount of energy dissipation required to form the damage zone at the crack tip, as well as a kinetic contrast between the rapid crack extension through the yielding zone (slip process) and the slow formation of a new yielding zone controlled by the external loading rate (stick process).

Force decomposition and toughness estimation from puncture experiments in soft solids

Several medical applications, like drug delivery and biosensing, are critically preceded by the insertion of needles and microneedles into biological tissue. However, the mechanical process of needle insertions, especially at high velocities, is currently not fully understood. Here, we explore the insertion of hollow needles into transparent silicone samples with an insertion velocity v ranging from 0.1 mm s-1 to 2.3 m s-1 (with needle radius R = 101.5 μm, thus strain rates ∼v/R ranging from 1 s-1 to 2.3 × 104 s-1). We use a double-insertion method, where the needle is inserted and re-inserted at the same location, to estimate the fracture properties of the material. The deflection of the specimen's free surface is found to be different between insertion and re-insertion experiments for identical needle positions, which is associated with different force magnitudes between insertion/reinsertion. This aspect was previously neglected in the original double-insertion method, thus here we develop a method based on imaging, image analyses and force measurements to decompose the measured force into individual force components, including deflection force Fd, frictional and spreading force Ff + Fs, and cutting force Ft. We estimate that the toughness Γ of our silicone samples, calculated using the cutting force Ft and the crack dimensions, increases with needle velocity, and ranges within observed values in previous literature for the same material and for some soft biological materials. In addition to toughness Γ, other parameters, such as critical force Fc and mechanical work Wc, also show strain-rate dependence, suggesting tissue stiffening, due to accumulated strain energy, at high speeds.

Toughening Hydrogels with Fibrillar Connected Double Networks

Biological tissues, such as tendons or cartilage, possess high strength and toughness with very low plastic deformations. In contrast, current strategies to prepare tough hydrogels commonly utilize energy dissipation mechanisms based on physical bonds that lead to irreversible large plastic deformations, thus limiting their load-bearing applications. This article reports a strategy to toughen hydrogels using fibrillar connected double networks (fc-DN), which consist of two distinct but chemically interconnected polymer networks, that is, a polyacrylamide network and an acrylated agarose fibril network. The fc-DN design allows efficient stress transfer between the two networks and high fibril alignment during deformation, both contributing to high strength and toughness, while the chemical crosslinking ensures low plastic deformations after undergoing high strains. The mechanical properties of the fc-DN network can be readily tuned to reach an ultimate tensile strength of 8 MPa and a toughness of above 55 MJ m-3, which is 3 and 3.5 times more than that of fibrillar double network hydrogels without chemical connections, respectively. The application potential of the fc-DN hydrogel is demonstrated as load-bearing damping material for a jointed robotic lander. The fc-DN design provides a new toughening mechanism for hydrogels that can be used for soft robotics or bioelectronic applications.

An Organic-Inorganic Hydrogel with Exceptional Mechanical Properties via Anion-Induced Synergistic Toughening for Accelerating Osteogenic Differentiation

Mineralized bio-tissues achieve exceptional mechanical properties through the assembly of rigid inorganic minerals and soft organic matrices, providing abundant inspiration for synthetic materials. Hydrogels, serving as an ideal candidate to mimic the organic matrix in bio-tissues, can be strengthened by the direct introduction of minerals. However, this enhancement often comes at the expense of toughness due to interfacial mismatch. This study reveals that extreme toughening of hydrogels can be realized through simultaneous in situ mineralization and salting-out, without the need for special chemical modification or additional reinforcements. The key to this strategy lies in harnessing the kosmotropic and precipitation behavior of specific anions as they penetrate a hydrogel system containing both anion-sensitive polymers and multivalent cations. The resulting mineralized hydrogels demonstrate significant improvements in fracture stress, fracture energy, and fatigue threshold due to a multiscale energy dissipation mechanism, with optimal values reaching 12 MPa, 49 kJ m-2, and 2.98 kJ m-2. This simple strategy also proves to be generalizable to other anions, resulting in tough hydrogels with osteoconductivity for promoting in vitro mineralization of human adipose-derived mesenchymal stem cells. This work introduces a universal route to toughen hydrogels without compromising other parameters, holding promise for biological applications demanding integrated mechanical properties.

Fibrin clot fracture under cyclic fatigue and variable rate loading

Fibrin clot is a vital class of fibrous materials, governing the mechanical response of blood clots. Fracture behavior of fibrin clots under complex physiological load is relevant for hemostasis and thrombosis. But how they fracture under cyclic and variable rate loading has not been reported. Here we conduct cyclic fatigue and monotonic variable rate loading tests on fibrin clots to characterize their fracture properties in terms of fatigue threshold and rate-dependent fracture toughness. We demonstrate that the fracture behavior of fibrin clots is sensitive to the amplitude of cyclic load and the loading rate. The cyclic fatigue tests show the fatigue threshold of fibrin clots at 1.66 J/m2, compared to the overall fracture toughness 15.8 J/m2. Furthermore, we rationalize the fatigue threshold using a semi-empirical model parameterized by 3D morphometric quantification to account for the hierarchical molecular structure of fibrin fibers. The variable loading tests reveal rate dependence of the overall fracture toughness of fibrin clots. Our analysis with a viscoelastic fracture model suggests the viscoelastic origin of the rate-dependent fracture toughness. The toughening mechanism of fibrin clots is further compared with biological tissues and hydrogels. This study advances the understanding and modeling of fatigue and fracture of blood clots and would motivate further investigation on the mechanics of fibrous materials. STATEMENT OF SIGNIFICANCE: Fibrin clot is a soft fibrous gel, exhibiting nonlinear mechanical responses under complex physiological loads. It is the main load-bearing constituent of blood clots where red blood cells, platelets and other cells are trapped. How the fibrin clot fractures under complex mechanical loads is critical for hemostasis and thrombosis. We study the fracture behavior of fibrin clots under cyclic fatigue and monotonic variable rate loads. We characterize the fatigue-threshold and viscous energy dissipation of fibrin clots. We compare the toughness enhancement of fibrin clots with hydrogels. The findings offer new insights into the fatigue and fracture of blood clots and fibrous materials, which could improve design guidelines for bioengineered materials.

Fracture-Resistant Stretchable Materials: An Overview from Methodology to Applications

Stretchable materials, such as gels and elastomers, are attractive materials in diverse applications. Their versatile fabrication platforms enable the creation of materials with various physiochemical properties and geometries. However, the mechanical performance of traditional stretchable materials is often hindered by the deficiencies in their energy dissipation system, leading to lower fracture resistance and impeding their broader range of applications. Therefore, the synthesis of fracture-resistant stretchable materials has attracted great interest. This review comprehensively summarizes key design considerations for constructing fracture-resistant stretchable materials, examines their synthesis strategies to achieve elevated fracture energy, and highlights recent advancements in their potential applications.

Insight into the fracture energy dissipation mechanism in elastomer composites via sacrificial bonds and fillers

Most tough elastomer composites are reinforced by introducing sacrificial structures and fillers. Understanding the contribution of fillers and sacrificial bonds in elastomer composites to the energy dissipation is critical for the design of high-toughness materials. However, the energy dissipation mechanism in elastomer composites remains elusive. In this study, using a tearing test and time-temperature superposition, we investigate the effect of fillers and sacrificial bonds on the energy dissipation of elastomer composites consisting of poly(lipoic acid)/silver-coated Al fillers. We found that the fillers and sacrificial bonds mutually enhance both the intrinsic fracture energy and the bulk energy dissipation, and moreover the sacrificial bonds play a more important role in enhancing fracture toughness than the fillers. It is unreasonable to rely solely on the loss factor for bulk energy dissipation. The addition of sacrificial bonds results in a chain segment experiencing greater binding force compared to the addition of fillers. This suggests that the chain segment consumes more energy during its movement. By calculating the length of the Kuhn chain segment and the Kuhn number, it is evident that the addition of sacrificial bonds results in a greater binding force for the chain segment than the addition of fillers, and this enhanced binding force increases the energy consumption during the motion of the chain segment.

Effect of Predamage on the Fracture Energy of Double-Network Hydrogels

Double-network (DN) hydrogels are tough soft materials, and the high fracture resistance can be attributed to the formation of a large damage zone (internal fracture of the brittle first network) around the crack tip. In this work, we studied the effect of predamage in the brittle network on the fracture energy Γc of DN hydrogels. The prestretch of the first network was induced by prestretching the DN gels to prestretch ratio λpre. Depending on the λpre in relative to the yielding stretch ratio λy, above which the brittle first network starts to break into discontinuous fragments inside DN gels, two regimes were observed: Γc decreases monotonically with λpre in the regime of λpre < λy, mainly due to the decreasing contribution from the bulk internal damage, while Γc increases with λpre in the regime of λpre > λy. The latter can be understood by the release of the hidden length of the stretchable network strands by the rupture of the brittle network, whereby the broken fragments of the brittle network could serve as sliding cross-links to further delocalize the stress-concentration near the crack tip and prevent chain scissions.

Strain-induced crystallization and phase separation used for fabricating a tough and stiff slide-ring solid polymer electrolyte

The demand for mechanically robust polymer-based electrolytes is increasing for applications to wearable devices. Young's modulus and breaking energy are essential parameters for describing the mechanical reliability of electrolytes. The former plays a vital role in suppressing the short circuit during charge-discharge, while the latter indicates crack propagation resistance. However, polymer electrolytes with high Young's moduli are generally brittle. In this study, a tough slide-ring solid polymer electrolyte (SR-SPE) breaking through this trade-off between stiffness and toughness is designed on the basis of strain-induced crystallization (SIC) and phase separation. SIC makes the material highly tough (breaking energy, 80 to 100 megajoules per cubic meter). Phase separation in the polymer enhanced stiffness (Young's modulus, 10 to 70 megapascals). The combined effect of phase separation and SIC made SR-SPE tough and stiff, while these mechanisms do not impair ionic conductivity. This SIC strategy could be combined with other toughening mechanisms to design tough polymer gel materials.

Fractographic mirror law for brittle fracture of nonlinear elastic soft materials

Mirror radius analysis of fractured surfaces is a powerful fractographic method for determining the cause of failure in linear elastic hard materials because it does not require prior loading information. However, mirror analysis for soft materials is lacking. In this study, we established a general mirror radius law for nonlinear elastic soft materials using highly deformable brittle hydrogels. The fracture stress and mirror radius follow a -1 power law, which differs from the -0.5 power law for linear elastic hard materials. The constant in the power law is related to the fracture energy of the material. This discovery provides insights into fracture mechanisms and leads the way for applying fractography to soft materials.

Humanoid Intelligent Display Platform for Audiovisual Interaction and Sound Identification

This study proposes a rational strategy for the design, fabrication and system integration of the humanoid intelligent display platform (HIDP) to meet the requirements of highly humanized mechanical properties and intelligence for human-machine interfaces. The platform's sandwich structure comprises a middle light-emitting layer and surface electrodes, which consists of silicon elastomer embedded with phosphor and silk fibroin ionoelastomer, respectively. Both materials are highly stretchable and resilient, endowing the HIDP with skin-like mechanical properties and applicability in various extreme environments and complex mechanical stimulations. Furthermore, by establishing the numerical correlation between the amplitude change of animal sounds and the brightness variation, the HIDP realizes audiovisual interaction and successful identification of animal species with the aid of Internet of Things (IoT) and machine learning techniques. The accuracy of species identification reaches about 100% for 200 rounds of random testing. Additionally, the HIDP can recognize animal species and their corresponding frequencies by analyzing sound characteristics, displaying real-time results with an accuracy of approximately 99% and 93%, respectively. In sum, this study offers a rational route to designing intelligent display devices for audiovisual interaction, which can expedite the application of smart display devices in human-machine interaction, soft robotics, wearable sound-vision system and medical devices for hearing-impaired patients.

Reinforcing Hydrogel by Nonsolvent-Quenching-Facilitated In Situ Nanofibrosis

Nanofibrous hydrogels are pervasive in load-bearing soft tissues, which are believed to be key to their extraordinary mechanical properties. Enlighted by this phenomenon, a novel reinforcing strategy for polymeric hydrogels is proposed, where polymer segments in the hydrogels are induced to form nanofibers in situ by bolstering their controllable aggregation at the nanoscale level. Poly(vinyl alcohol) hydrogels are chosen to demonstrate the virtue of this strategy. A nonsolvent-quenching step is introduced into the conventional solvent-exchange hydrogel preparation approach, which readily promotes the formation of nanofibrous hydrogels in the following solvent-tempering process. The resultant nanofibrous hydrogels demonstrate significantly improved mechanical properties and swelling resistance, compared to the conventional solvent-exchange hydrogels with identical compositions. This work validates the hypothesis that bundling polymer chains to form nanofibers can lead to nanofibrous hydrogels with remarkably enhanced mechanical performances, which may open a new horizon for single-component hydrogel reinforcement.

Crack propagation and arrests in gelatin hydrogels are linked to tip curvatures

Gelatin hydrogels are attractive scaffold materials for tissue engineering applications as they provide motifs for cell attachment, undergo large deformations, and are tunable. Low toughness and brittle fractures however limit their use in load bearing applications. An investigation of crack tip processes and mechanisms of crack propagation is warranted to link fracture properties with material microstructure. We cross-linked gelatin using glutaraldehyde to obtain low cross-linked control hydrogels and used an additional cross-linker, methylglyoxal, to fabricate MGO hydrogels with higher cross-links. We quantified fractures in the gelatin hydrogels from both groups using pure shear notch tests and characterized strain fields near the crack tip using 2-D digital image correlation. We used a numerical method based on Taylor's series expansion to measure the crack tip curvatures in the hydrogels. This method captures tip curvatures better than the parabolic method routinely used in studies. Results from our study show that cracks in gelatin hydrogels underwent frequent arrests during propagation through the specimen width in both groups. MGO hydrogels had 85% enhanced fracture toughness and a significantly higher number of stalls compared to the control group. Crack initiations following stalls in the sample correlated with low tip curvatures in both hydrogel groups. We also show that mechanical stretching blunts the crack tip before crack propagation; the degree of blunting was independent of the cross-link density and elastic modulus of the gelatin hydrogels. These results show a link between crack growth and the tip curvature in cross-linked gelatin hydrogels, and offer potential insights for the development of tougher hydrogels.

Puncturing of soft tissues: experimental and fracture mechanics-based study

The integrity of soft materials against puncturing is of great relevance for their performance because of the high sensitivity to local rupture caused by rigid sharp objects. In this work, the mechanics of puncturing is studied with respect to a sharp-tipped rigid needle with a circular cross section, penetrating a soft target solid. The failure mode associated with puncturing is identified as a mode-I crack propagation, which is analytically described by a two-dimensional model of the target solid, taking place in a plane normal to the penetration axis. It is shown that the force required for the onset of needle penetration is dependent on two energy contributions, that are, the strain energy stored in the target solid and the energy consumed in crack propagation. More specifically, the force is found to be dependent on the fracture toughness of the material, its stiffness and the sharpness of the penetrating tool. The reference case within the framework of small strain elasticity is first investigated, leading to closed-form toughness parameters related to classical linear elastic fracture mechanics. Then, nonlinear finite element analyses for an Ogden hyperelastic material are presented. Supporting the proposed theoretical framework, a series of puncturing experiments on two commercial silicones is presented. The combined experimental-theoretical findings suggest a simple, yet reliable tool to easily handle and assess safety against puncturing of soft materials.

The Ogden model for hydrogels in tissue engineering: Modulus determination with compression to failure

Hydrogel mechanical properties for tissue engineering are often reported in terms of a compressive elastic modulus derived from a linear regression of a typically non-linear stress-strain plot. There is a need for an alternative model to fit the full strain range of tissue engineering hydrogels. Fortunately, the Ogden model provides a shear modulus, μ₀, and a nonlinear parameter, α, for routine analysis of compression to failure. Three example hydrogels were tested: (1) pentenoate-modified hyaluronic acid (PHA), (2) dual-crosslinked PHA and polyethylene glycol diacrylate (PHA-PEGDA), and (3) composite PHA-PEGDA hydrogel with cryoground devitalized cartilage (DVC) at 5, 10, and 15%w/v concentration (DVC5, DVC10, and DVC15, respectively). Gene expression analyses suggested that the DVC hydrogels supported chondrogenesis of human bone marrow mesenchymal stem cells to some degree. Both linear regression (5 to 15% strain) and Ogden fits (to failure) were performed. The compressive elastic modulus, E, was over 4-fold higher in the DVC15 group relative to the PHA group (129 kPa). Similarly, the shear modulus, μ₀, was over 3-fold higher in the DVC15 group relative to the PHA group (37 kPa). The PHA group exhibited a much higher degree of nonlinearity (α = 10) compared to the DVC15 group (α = 1.4). DVC hydrogels may provide baseline targets of μ₀ and α for future cartilage tissue engineering studies. The Ogden model was demonstrated to fit the full strain range with high accuracy (R² = 0.998 ± 0.001) and to quantify nonlinearity. The current study provides an Ogden model as an attractive alternative to the elastic modulus for tissue engineering constructs.

Micromechanics and damage in slide-ring networks

We explore the mechanics and damage of slide-ring gels by developing a discrete model for the mechanics of chain-ring polymer systems that accounts for both crosslink motion and internal chain sliding. The proposed framework utilizes an extendable Langevin chain model to describe the constitutive behavior of polymer chains undergoing large deformation and includes a rupture criterion to innately capture damage. Similarly, crosslinked rings are described as large molecules that also store enthalpic energy during deformation and thus have their own rupture criterion. Using this formalism, we show that the realized mode of damage in a slide-ring unit is a function of the loading rate, distribution of segments, and inclusion ratio (number of rings per chain). After analyzing an ensemble of representative units under different loading conditions, we find that failure is driven by damage to crosslinked rings at slow loading rates, but polymer chain scission at fast loading rates. Our results indicate that increasing the strength of the crosslinked rings may improve the toughness of the material.

Dynamic interaction of injected liquid jet with skin layer interfaces revealed by microsecond imaging of optically cleared ex vivo skin tissue model

BACKGROUND

Needle-free jet injection (NFJI) systems enable a controlled and targeted delivery of drugs into skin tissue. However, a scarce understanding of their underlying mechanisms has been a major deterrent to the development of an efficient system. Primarily, the lack of a suitable visualization technique that could capture the dynamics of the injected fluid-tissue interaction with a microsecond range temporal resolution has emerged as a main limitation. A conventional needle-free injection system may inject the fluids within a few milliseconds and may need a temporal resolution in the microsecond range for obtaining the required images. However, the presently available imaging techniques for skin tissue visualization fail to achieve these required spatial and temporal resolutions. Previous studies on injected fluid-tissue interaction dynamics were conducted using in vitro media with a stiffness similar to that of skin tissue. However, these media are poor substitutes for real skin tissue, and the need for an imaging technique having ex vivo or in vivo imaging capability has been echoed in the previous reports.

METHODS

A near-infrared imaging technique that utilizes the optical absorption and fluorescence emission of indocyanine green dye, coupled with a tissue clearing technique, was developed for visualizing a NFJI in an ex vivo porcine skin tissue.

RESULTS

The optimal imaging conditions obtained by considering the optical properties of the developed system and mechanical properties of the cleared ex vivo samples are presented. Crucial information on the dynamic interaction of the injected liquid jet with the ex vivo skin tissue layers and their interfaces could be obtained.

CONCLUSIONS

The reported technique can be instrumental for understanding the injection mechanism and for the development of an efficient transdermal NFJI system as well.

Strong, Chemically Stable, and Enzymatically On-Demand Detachable Hydrogel Adhesion Using Protein Crosslink

Achieving strong adhesion between hydrogels and diverse materials is greatly significant for emerging technologies yet remains challenging. Existing methods using non-covalent bonds have limited pH and ion stability, while those using covalent bonds typically lack on-demand detachment capability, limiting their applications. In this study, a general strategy of covalent bond-based and detachable adhesion by incorporating amine-rich proteins in various hydrogels and inducing the interfacial crosslinking of the hydrogels using a protein-crosslinking agent is demonstrated. The protein crosslink offers topological adhesion and can reach a strong adhesion energy of ≈750 J m^-2 . The chemistry of the adhesion is characterized and that the inclusion of proteins inside the hydrogels does not alter the hydrogels' properties is shown. The adhesion remains intact after treating the adhered hydrogels with various pH solutions and ions, even at an elevated temperature. The detachment is triggered by treating proteinase solution at the bonding front, causing the digestion of proteins, thus breaking up the interfacial crosslink network. In addition, that this approach can be used to adhere hydrogels to diverse dry surfaces, including glass, elastomers and plastics, is shown. The stable chemistry of protein crosslinks opens the door for various applications in a wide range of chemical environments.

Green multifunctional PVA composite hydrogel-membrane for the efficient purification of emulsified oil wastewater containing Pb2+ ions

To date, most existing engineering materials have difficulty simultaneously separating oil/water and removing heavy metals from complex oily wastewater. In response to this challenge, a novel multifunctional composite hydrogel membrane (named PVA-CS-LDHs) was fabricated by incorporating chitosan (CS) and nanohydrotalcite (LDHs) into a polyvinyl alcohol (PVA) hydrogel. This material was developed using an easy yet versatile strategy of freezing and salting-out, which can enable the formation of a PVA-CS-LDH hydrogel membrane in one step and endow the PVA-CS-LDHs with high strength, excellent stretchability, favourable shape recoverability, and an ideal 3D microstructure. The PVA-CS-LDH membrane can purify emulsified oil and metal ions simultaneously with a separation efficiency of 99.89 % for emulsified oil and a removal efficiency of 97.44 % for Pb2+ ions. Additionally, the high-efficiency, multifunctional, high-antifouling and eco-friendly properties of the PVA-CS-LDH membrane make it a promising hydrogel material for both emulsified oil separation and heavy metal ion removal. Thus, this material provides critical application potential that can address scientific and technological challenges in complex oily wastewater purification.

Peptide-enhanced tough, resilient and adhesive eutectogels for highly reliable strain/pressure sensing under extreme conditions

Natural gels and biomimetic hydrogel materials have been able to achieve outstanding integrated mechanical properties due to the gain of natural biological structures. However, nearly every natural biological structure relies on water as solvents or carriers, which limits the possibility in extreme conditions, such as sub-zero temperatures and long-term application. Here, peptide-enhanced eutectic gels were synthesized by introducing α-helical "molecular spring" structure into deep eutectic solvent. The gel takes full advantage of the α-helical structure, achieving high tensile/compression, good resilience, superior fracture toughness, excellent fatigue resistance and strong adhesion, while it also inherits the benefits of the deep eutectic solvent and solves the problems of solvent volatilization and freezing. This enables unprecedentedly long and stable sensing of human motion or mechanical movement. The electrical signal shows almost no drift even after 10,000 deformations for 29 hours or in the -20 °C to 80 °C temperature range.

Modelling biological puncture: a mathematical framework for determining the energetics and scaling

Biological puncture systems use a diversity of morphological tools (stingers, teeth, spines etc.) to penetrate target tissues for a variety of functions (prey capture, defence, reproduction). These systems are united by a set of underlying physical rules which dictate their mechanics. While previous studies have illustrated form-function relationships in individual systems, these underlying rules have not been formalized. We present a mathematical model for biological puncture events based on energy balance that allows for the derivation of analytical scaling relations between energy expenditure and shape, size and material response. The model identifies three necessary energy contributions during puncture: fracture creation, elastic deformation of the material and overcoming friction during penetration. The theoretical predictions are verified using finite-element analyses and experimental tests. Comparison between different scaling relationships leads to a ratio of released fracture energy and deformation energy contributions acting as a measure of puncture efficiency for a system that incorporates both tool shape and material response. The model represents a framework for exploring the diversity of biological puncture systems in a rigorous fashion and allows future work to examine how fundamental physical laws influence the evolution of these systems.

Hydroelastomers: soft, tough, highly swelling composites

Inspired by the cellular design of plant tissue, we present an approach to make versatile, tough, highly water-swelling composites. We embed highly swelling hydrogel particles inside tough, water-permeable, elastomeric matrices. The resulting composites, which we call hydroelastomers, combine the properties of their parent phases. From their hydrogel component, the composites inherit the ability to highly swell in water. From the elastomeric component, the composites inherit excellent stretchability and fracture toughness, while showing little softening as they swell. Indeed, the fracture properties of the composite match those of the best-performing, tough hydrogels, exhibiting fracture energies of up to 10 kJ m^-2. Our composites are straightforward to fabricate, based on widely-available materials, and can easily be molded or extruded to form shapes with complex swelling geometries. Furthermore, there is a large design space available for making hydroelastomers, since one can use any hydrogel as the dispersed phase in the composite, including hydrogels with stimuli-responsiveness. These features make hydroelastomers excellent candidates for use in soft robotics and swelling-based actuation, or as shape-morphing materials, while also being useful as hydrogel replacements in other fields.

Advanced cellulose nanocrystals (CNC) and cellulose nanofibrils (CNF) aerogels: Bottom-up assembly perspective for production of adsorbents

The most common and abundant polymer in nature is the linear polysaccharide cellulose, but processing it requires a new approach since cellulose degrades before melting and does not dissolve in ordinary organic solvents. Cellulose aerogels are exceptionally porous (>90 %), have a high specific surface area, and have low bulk density (0.0085 mg/cm³), making them suitable for a variety of sophisticated applications including but not limited to adsorbents. The production of materials with different qualities from the nanocellulose based aerogels is possible thanks to the ease with which other chemicals may be included into the structure of nanocellulose based aerogels; despite processing challenges, cellulose can nevertheless be formed into useful, value-added products using a variety of traditional and cutting-edge techniques. To improve the adsorption of these aerogels, rheology, 3-D printing, surface modification, employment of metal organic frameworks, freezing temperature, and freeze casting techniques were all investigated and included. In addition to exploring venues for creation of aerogels, their integration with CNC liquid crystal formation were also explored and examined to pursue "smart adsorbent aerogels". The objective of this endeavour is to provide a concise and in-depth evaluation of recent findings about the conception and understanding of nanocellulose aerogel employing a variety of technologies and examination of intricacies involved in enhancing adsorption properties of these aerogels.

Anisotropic damage model for collagenous tissues and its application to model fracture and needle insertion mechanics

The analysis of tissue mechanics in biomedical applications demands nonlinear constitutive models able to capture the energy dissipation mechanisms, such as damage, that occur during tissue deformation. Furthermore, implementation of sophisticated material models in finite element models is essential to improve medical devices and diagnostic tools. Building on previous work toward microstructure-driven models of collagenous tissue, here we show a constitutive model based on fiber orientation and waviness distributions for skin that captures not only the anisotropic strain-stiffening response of this and other collagen-based tissues, but, additionally, accounts for tissue damage directly as a function of changes in the microstructure, in particular changes in the fiber waviness distribution. The implementation of this nonlinear constitutive model as a user subroutine in the popular finite element package Abaqus enables large-scale finite element simulations for biomedical applications. We showcase the performance of the model in fracture simulations during pure shear tests, as well as simulations of needle insertion into skin relevant to auto-injector design.

Modeling Tunable Fracture in Hydrogel Shell Structures for Biomedical Applications

Hydrogels are nowadays widely used in various biomedical applications, and show great potential for the making of devices such as biosensors, drug- delivery vectors, carriers, or matrices for cell cultures in tissue engineering, etc. In these applications, due to the irregular complex surface of the human body or its organs/structures, the devices are often designed with a small thickness, and are required to be flexible when attached to biological surfaces. The devices will deform as driven by human motion and under external loading. In terms of mechanical modeling, most of these devices can be abstracted as shells. In this paper, we propose a mixed graph-finite element method (FEM) phase field approach to model the fracture of curved shells composed of hydrogels, for biomedical applications. We present herein examples for the fracture of a wearable biosensor, a membrane-coated drug, and a matrix for a cell culture, each made of a hydrogel. Used in combination with experimental material testing, our method opens a new pathway to the efficient modeling of fracture in biomedical devices with surfaces of arbitrary curvature, helping in the design of devices with tunable fracture properties.

Tough Wet Adhesion of Hydrogen-Bond-Based Hydrogel with On-Demand Debonding and Efficient Hemostasis

Hydrogels have been widely used in wet tissues. However, the insufficient adhesion of hydrogels for wound hemostasis remains a grand challenge. Herein, a facile yet effective strategy is developed to fabricate tough wet adhesion of hydrogen-bond-based hydrogel (PAAcVI hydrogel) using copolymerization of acrylic acid and 1-vinylimidazole in dimethyl sulfoxide followed by solvent exchange with water. The PAAcVI hydrogel shows equally robust adhesion (>400 J m^-2) to both wet and dry tissues. Moreover, the PAAcVI hydrogel also exhibits strong long-term stable adhesion underwater and in various wet environments. Meanwhile, the adhesion of PAAcVI hydrogel can be adjusted through Zn²⁺-ion-mediated on-demand debonding, which makes it easy to peel off from the tissue reducing pain during dressing removal and avoiding secondary injury. The PAAcVI hydrogel displays efficient hemostasis in the mice-tail docking model and mice-liver bleeding model. This hydrogen-bond-based hydrogel shows tough wet adhesion, and its adhesion is controllable, demonstrating its promising application in moisture-resistant adhesives, medical adhesives, and hemostatic materials.

An extreme toughening mechanism for soft materials

Soft yet tough materials are ubiquitous in nature and everyday life. The ratio between fracture toughness and intrinsic fracture energy of a soft material defines its toughness enhancement. Soft materials' toughness enhancement has been long attributed to their bulk stress-stretch hysteresis induced by dissipation mechanisms such as Mullins effect and viscoelasticity. With a combination of experiments and theory, here we show that the bulk dissipation mechanisms significantly underestimate the toughness enhancement of soft tough materials. We propose a new mechanism and scaling law to account for extreme toughening of diverse soft materials. We show that the toughness enhancement of soft materials relies on both bulk hysteretic dissipation, and near-crack dissipation due to mechanisms such as polymer-chain entanglement. Unlike the bulk hysteretic dissipation, the near-crack dissipation does not necessarily induce large stress-stretch hysteresis of the bulk material. The extreme toughening mechanism can be potentially universally applied to various soft tough materials, ranging from double-network hydrogels, interpenetrating-network hydrogels, entangled-network hydrogels and slide-ring hydrogels, to unfilled and filled rubbers.

Cavitation induced fracture of intact brain tissue

Nonpenetrating traumatic brain injuries (TBIs) are linked to cavitation. The structural organization of the brain makes it particularly susceptible to tears and fractures from these cavitation events, but limitations in existing characterization methods make it difficult to understand the relationship between fracture and cavitation in this tissue. More broadly, fracture energy is an important, yet often overlooked, mechanical property of all soft tissues. We combined needle-induced cavitation with hydraulic fracture models to induce and quantify fracture in intact brains at precise locations. We report here the first measurements of the fracture energy of intact brain tissue that range from 1.5 to 8.9 J/m2, depending on the location in the brain and the model applied. We observed that fracture consistently occurs along interfaces between regions of brain tissue. These fractures along interfaces allow cavitation-related damage to propagate several millimeters away from the initial injury site. Quantifying the forces necessary to fracture brain and other soft tissues is critical for understanding how impact and blast waves damage tissue in vivo and has implications for the design of protective gear and tissue engineering.

Role of dynamic bonds on fatigue threshold of tough hydrogels

SignificanceDynamic bonds have been found to enhance fracture toughness of hydrogels as sacrificial bonds, but the role of dynamic bonds to fatigue threshold of hydrogels is poorly understood because the wide dynamic range of viscoelastic response imposes a challenge on fatigue experiments. Here, by using polyampholyte hydrogels, we adopted a time-salt superposition principle to access a wide range of time scales that are otherwise difficult to access in fatigue tests. Relations between fatigue threshold and strain rate in elastic and viscoelastic regimes and the corresponding mechanism correlated to permanent/dynamic bonds were revealed. We believe that this work gives important insight into the design and development of fatigue-resistant soft materials composed of dynamic bonds.

Stretchy and disordered: Toward understanding fracture in soft network materials via mesoscopic computer simulations

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. In addition, in colloidal gels, an underlying network structure can be identified, and several metamaterials and textiles can be considered network materials as well. Many of these materials share a highly disordered microstructure and can undergo large deformations before damage becomes visible at the macroscopic level. Despite their widespread presence, we still lack a clear picture of how the network structure controls the fracture processes of these soft materials. In this Perspective, we will focus on progress and open questions concerning fracture at the mesoscopic scale, in which the network architecture is clearly resolved, but neither the material-specific atomistic features nor the macroscopic sample geometries are considered. We will describe concepts regarding the network elastic response that have been established in recent years and turn out to be pre-requisites to understand the fracture response. We will mostly consider simulation studies, where the influence of specific network features on the material mechanics can be cleanly assessed. Rather than focusing on specific systems, we will discuss future challenges that should be addressed to gain new fundamental insights that would be relevant across several examples of soft network materials.

Double-Network Tough Hydrogels: A Brief Review on Achievements and Challenges

This brief review attempts to summarize research advances in the mechanical toughness and structures of double-network (DN) hydrogels. The focus is to provide a critical and concise discussion on the toughening mechanisms, damage recoverability, stress relaxation, and biomedical applications of tough DN hydrogel systems. Both conventional DN hydrogel with two covalently cross-linked networks and novel DN systems consisting of physical and reversible cross-links are discussed and compared. Covalently cross-linked hydrogels are tough but damage-irreversible. Physically cross-linked hydrogels are damage-recoverable but exhibit mechanical instability, as reflected by stress relaxation tests. This remains one significant challenge to be addressed by future research studies to realize the load-sustaining applications proposed for tough hydrogels. With their special structure and superior mechanical properties, DN hydrogels have great potential for biomedical applications, and many DN systems are now fabricated with 3D printing techniques.

Humidity dependence of fracture toughness of cellulose fibrous networks

Cellulose-based materials are increasingly finding applications in technology due to their sustainability and biodegradability. The sensitivity of cellulose fiber networks to environmental conditions such as temperature and humidity is well known. Yet, there is an incomplete understanding of the dependence of the fracture toughness of cellulose networks on environmental conditions. In the current study, we assess the effect of moisture content on the out-of-plane (i.e., z-dir.) fracture toughness of a particular cellulose network, specifically Whatman cellulose filter paper. Experimental measurements are performed at 16% RH along the desorption isotherm and 23, 37, 50, 75% RH along the adsorption isotherm using out-of-plane tensile tests and double cantilever beam (DCB) tests. Cohesive zone modeling and finite element simulations are used to extract quantitative properties that describe the crack growth behavior. Overall, the fracture toughness of filter paper decreased with increasing humidity. Additionally, a novel model is developed to capture the high peak and sudden drop in the experimental force measurement caused by the existence of an initiation region. This model is found to be in good agreement with experimental data. The relative effect of each independent cohesive parameter is explored to better understand the cohesive zone-based humidity dependence model. The methods described here may be applied to study rupture of other fiber networks with weak bonds.

Highly Durable and Tough Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are soft materials that exhibit interesting anisotropic and actuation properties. The emerging applications of thermally actuatable LCEs demand sufficient mechanical durability under various thermomechanical cycles. Although LCEs are tough at room temperature, they become very brittle at high temperature (above their actuation temperature), which can cause unexpected failure. We demonstrate a strategy to improve the high temperature fracture and fatigue properties of LCEs by designing interpenetrating polymer networks using a second polyurethane network. By selecting the appropriate composition of the polyurethane networks, the high temperature fracture and fatigue properties of LCEs were significantly enhanced, while retaining their actuation properties. The strategy from this work will help fabricate LCE-based actuators that are tough and durable at high temperatures and under cyclic loading.

Drug Delivery Based on Stimuli-Responsive Injectable Hydrogels for Breast Cancer Therapy: A Review

Breast cancer is the most common and biggest health threat for women. There is an urgent need to develop novel breast cancer therapies to overcome the shortcomings of conventional surgery and chemotherapy, which include poor drug efficiency, damage to normal tissues, and increased side effects. Drug delivery systems based on injectable hydrogels have recently gained remarkable attention, as they offer encouraging solutions for localized, targeted, and controlled drug release to the tumor site. Such systems have great potential for improving drug efficiency and reducing the side effects caused by long-term exposure to chemotherapy. The present review aims to provide a critical analysis of the latest developments in the application of drug delivery systems using stimuli-responsive injectable hydrogels for breast cancer treatment. The focus is on discussing how such hydrogel systems enhance treatment efficacy and incorporate multiple breast cancer therapies into one system, in response to multiple stimuli, including temperature, pH, photo-, magnetic field, and glutathione. The present work also features a brief outline of the recent progress in the use of tough hydrogels. As the breast undergoes significant physical stress and movement during sporting and daily activities, it is important for drug delivery hydrogels to have sufficient mechanical toughness to maintain structural integrity for a desired period of time.

Nanoengineered biomimetic hydrogels: A major advancement to fabricate 3D-printed constructs for regenerative medicine

Nanostructured compounds already validated as performant reinforcements for biomedical applications together with different fabrication strategies have been often used to channel the biophysical and biochemical features of hydrogel networks. Ergo, a wide array of nanostructured compounds has been employed as additive materials integrated with hydrophilic networks based on naturally-derived polymers to produce promising scaffolding materials for specific fields of regenerative medicine. To date, nanoengineered hydrogels are extensively explored in (bio)printing formulations, representing the most advanced designs of hydrogel (bio)inks able to fabricate structures with improved mechanical properties and high print fidelity along with a cell-interactive environment. The development of printing inks comprising organic-inorganic hybrid nanocomposites is in full ascent as the impact of a small amount of nanoscale additive does not translate only in improved physicochemical and biomechanical properties of bioink. The biopolymeric nanocomposites may even exhibit additional particular properties engendered by nano-scale reinforcement such as electrical conductivity, magnetic responsiveness, antibacterial or antioxidation properties. The present review focus on hydrogels nanoengineered for 3D printing of biomimetic constructs, with particular emphasis on the impact of the spatial distribution of reinforcing agents (0D, 1D, 2D). Here, a systematic analysis of the naturally-derived nanostructured inks is presented highlighting the relationship between relevant length scales and size effects that influence the final properties of the hydrogels designed for regenerative medicine. This article is protected by copyright. All rights reserved.

How chain dynamics affects crack initiation in double-network gels

Double-network gels are a class of tough soft materials comprising two elastic networks with contrasting structures. The formation of a large internal damage zone ahead of the crack tip by the rupturing of the brittle network accounts for the large crack resistance of the materials. Understanding what determines the damage zone is the central question of the fracture mechanics of double-network gels. In this work, we found that at the onset of crack propagation, the size of necking zone, in which the brittle network breaks into fragments and the stretchable network is highly stretched, distinctly decreases with the increase of the solvent viscosity, resulting in a reduction in the fracture toughness of the material. This is in sharp contrast to the tensile behavior of the material that does not change with the solvent viscosity. This result suggests that the dynamics of stretchable network strands, triggered by the rupture of the brittle network, plays a role. To account for this solvent viscosity effect on the crack initiation, a delayed blunting mechanism regarding the polymer dynamics effect is proposed. The discovery on the role of the polymer dynamic adds an important missing piece to the fracture mechanism of this unique material.

Effects of solvent osmolarity and viscosity on cartilage energy dissipation under high-frequency loading

Articular cartilage is a spatially heterogeneous, dissipative biological hydrogel with a high fluid volume fraction. Although energy dissipation is important in the context of delaying cartilage damage, the dynamic behavior of articular cartilage equilibrated in media of varied osmolarity and viscosity is not widely understood. This study investigated the mechanical behaviors of cartilage when equilibrated to media of varying osmolarity and viscosity. Dynamic moduli and phase shift were measured at both low (1 Hz) and high (75-300 Hz) frequency, with cartilage samples compressed to varied offset strain levels. Increasing solution osmolarity and viscosity both independently resulted in larger energy dissipation and decreased dynamic modulus of cartilage at both low and high frequency. Mechanical property alterations induced by varying osmolarity are likely due to the change in permeability and fluid volume fraction within the tissue. The effects of solution viscosity are likely due to frictional interactions at the solid-fluid interface, affecting energy dissipation. These findings highlight the significance of interstitial fluid on the energy dissipation capabilities of the tissue, which can influence the onset of cartilage damage.

Why is mechanical fatigue different from toughness in elastomers? The role of damage by polymer chain scission

Although elastomers often experience 10 to 100 million cycles before failure, there is now a limited understanding of their resistance to fatigue crack propagation. We tagged soft and tough double-network elastomers with mechanofluorescent probes and quantified damage by sacrificial bond scission after crack propagation under cyclic and monotonic loading. Damage along fracture surfaces and its spatial localization depend on the elastomer design, as well as on the applied load (i.e., cyclic or monotonic). The key result is that reversible elasticity and strain hardening at low and intermediate strains dictates fatigue resistance, whereas energy dissipation at high strains controls toughness. This information serves to engineer fatigue-resistant elastomers, understand fracture mechanisms, and reduce the environmental footprint of the polymer industry.

Strength and deformability of fibrin clots: Biomechanics, thermodynamics, and mechanisms of rupture

Fibrin is the major determinant of the mechanical stability and integrity of blood clots and thrombi. To explore the rupture of blood clots, emulating thrombus breakage, we stretched fibrin gels with single-edge cracks of varying size. Ultrastructural alterations of the fibrin network correlated with three regimes of stress vs. strain profiles: the weakly non-linear regime due to alignment of fibrin fibers; linear regime owing to further alignment and stretching of fibers; and the rupture regime for large deformations reaching the critical strain and stress, at which irreversible breakage of fibers ahead of the crack tip occurs. To interpret the stress-strain curves, we developed a new Fluctuating Spring model, which maps the fibrin alignment at the characteristic strain, network stretching with the Young modulus, and simultaneous cooperative rupture of coupled fibrin fibers into a theoretical framework to obtain the closed-form expressions for the strain-dependent stress profiles. Cracks render network rupture stochastic, and the free energy change for fiber deformation and rupture decreases with the crack length, making network rupture more spontaneous. By contrast, mechanical cooperativity due to the presence of inter-fiber contacts strengthens fibrin networks. The results obtained provide a fundamental understanding of blood clot breakage that underlies thrombotic embolization. STATEMENT OF SIGNIFICANCE: Fibrin, a naturally occurring biomaterial, is the major determinant of mechanical stability and integrity of blood clots and obstructive thrombi. We tested mechanically fibrin gels with single-edge cracks and followed ultrastructural alterations of the fibrin network. Rupture of fibrin gel involves initial alignment and elastic stretching of fibers followed by their eventual rupture for deformations reaching the critical level. To interpret the stress-strain curves, we developed Fluctuating Spring model, which showed that cracks render rupture of fibrin networks more spontaneous; yet, coupled fibrin fibers reinforce cracked fibrin networks. The results obtained provide fundamental understanding of blood clot breakage that underlies thrombotic embolization. Fluctuating Spring model can be applied to other protein networks with cracks and to interpret the stress-strain profiles.

An experimental method for estimating the tearing energy in rubber-like materials using the true stored energy

A method for determining the critical tearing energy in rubber-like materials is proposed. In this method, the energy required for crack propagation in a rubber-like material is determined by the change of recovered elastic energy which is obtained by deducting the dissipated energy due to different inelastic processes from the total strain energy applied to the system. Hence, the classical method proposed by Rivlin and Thomas using the pure shear tear test is modified using the actual stored elastic energy. The total dissipated energy is evaluated using cyclic pure shear and simple shear dynamic experiments at the critical stretch level. To accurately estimate the total dissipated energy, the unloading rate is determined from the time the crack takes to grow an increment. A carbon-black-filled natural rubber is examined in this study. In cyclic pure shear experiment, the specimens were cyclically loaded under quasi-static loading rate of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.01~{\rm {s}}^{-1}$$\end{document}0.01s-1 and for different unloading rates, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.01$$\end{document}0.01, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.1$$\end{document}0.1 and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$1.0~{\rm {s}}^{-1}$$\end{document}1.0s-1. The simple shear dynamic experiment is used to obtain the total dissipated energy at higher frequencies, i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.5$$\end{document}0.5-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$18~{\rm {Hz}}$$\end{document}18Hz which corresponds to unloading rates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.46$$\end{document}0.46-\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$16.41~{\rm {s}}^{-1}$$\end{document}16.41s-1, using the similarities between simple and pure shear deformation. The relationship between dissipated energy and unloading stretch rate is found to follow a power-law such that cyclic pure shear and simple shear dynamic experiments yield similar result. At lower unloading rates (i.e. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{\lambda }}_{\rm {U}} < 1.0~{\rm {s}}^{-1}$$\end{document}λ˙U<1.0s-1), Mullins effect dominates and the viscous dissipation is minor, whereas at higher unloading rates, viscous dissipation becomes significant. At the crack propagation unloading rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$125.2~{\rm {s}}^{-1}$$\end{document}125.2s-1, the viscous dissipation is significant such that the amount of dissipated energy increases approximately by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$125.4\%$$\end{document}125.4% from the lowest unloading rate. The critical tearing energy is obtained to be \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$7.04~{\rm {kJ}}/{\rm {m}}^{2}$$\end{document}7.04kJ/m2 using classical method and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$5.12~{\rm {kJ}}/{\rm {m}}^{2}$$\end{document}5.12kJ/m2 using the proposed method. Hence, the classical method overestimates the critical tearing energy by approximately \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$37.5\%$$\end{document}37.5%.

On the relationship between cutting and tearing in soft elastic solids

Unique observations of cutting energy in silicone elastomers motivate a picture of soft fracture that qualitatively and quantitatively links far-field tearing with push cutting for the first time. For blades of decreasing tip radii, the cutting energy decreases until it reaches a plateau that suggests a threshold for failure. A super-molecular damage zone, necessary for new surface creation, is defined using the tip radius at the onset of this threshold. Modifying the classic Lake-Thomas theory, in which failure occurs within a molecular plane, to this super-molecular zone provides order-of-magnitude agreement with the cutting energy threshold. Together, the threshold fracture energy and damage length scale define criteria for failure that, when implemented in finite element simulation, quantitatively reproduce the increase in cutting energy with increasing blade radius outside of the plateau. The rate of increase depends on the constitutive response of the material, with more neo-Hookean solids requiring a larger failure force per incremental increase in blade radius as observed experimentally. This combination of a geometry-independent failure threshold (from the cutting energy plateau) and a need to account for the role of material deformability in the stress concentration found at the crack tip (from the rate of cutting energy increase with blade radius) align with the discovery of a new dimensionless group. This new parameter proportionally maps cutting energy to the energy required to tear a sample under far-field loading conditions by using ultimate properties obtained in uniaxial tension.

Stimulation Modulates Adhesion and Mechanics of Hydrogel Adhesives

The ability to modulate the adhesion of soft materials on-demand is desired for broad applications ranging from tissue repair to soft robotics. Research effort has been focused on the chemistry and architecture of interfaces, leaving the mechanics of soft adhesives overlooked. Stimuli-responsive mechanisms of smart hydrogels could be leveraged for achieving stimuli-responsive hydrogel adhesives that respond mechanically to external stimuli. Such stimuli-responsive hydrogel adhesives involve complex chemomechanical coupling and interfacial fracture phenomena, calling for mechanistic understanding to enable rational design. Here, we combine experimental, computational, and analytical approaches to study a thermo-responsive hydrogel adhesive. Experimentally, we show that the adhesion and mechanical properties of a stimuli-responsive hydrogel adhesive are both enhanced by the application of a stimulus. Our analysis further reveals that the enhanced adhesion stems from the increased fracture energy of the bulk hydrogel and the insignificant residual stress on the adhesive-tissue interface. This study presents a framework for designing stimuli-responsive hydrogel adhesives based on the modulation of bulk properties and sheds light on the development of smart adhesives with tunable mechanics.

Simultaneously Toughening and Stiffening Elastomers with Octuple Hydrogen Bonding

Current synthetic elastomers suffer from the well-known trade-off between toughness and stiffness. By a combination of multiscale experiments and atomistic simulations, a transparent unfilled elastomer with simultaneously enhanced toughness and stiffness is demonstrated. The designed elastomer comprises homogeneous networks with ultrastrong, reversible, and sacrificial octuple hydrogen bonding (HB), which evenly distribute the stress to each polymer chain during loading, thus enhancing stretchability and delaying fracture. Strong HBs and corresponding nanodomains enhance the stiffness by restricting the network mobility, and at the same time improve the toughness by dissipating energy during the transformation between different configurations. In addition, the stiffness mismatch between the hard HB domain and the soft poly(dimethylsiloxane)-rich phase promotes crack deflection and branching, which can further dissipate energy and alleviate local stress. These cooperative mechanisms endow the elastomer with both high fracture toughness (17016 J m^-2 ) and high Young's modulus (14.7 MPa), circumventing the trade-off between toughness and stiffness. This work is expected to impact many fields of engineering requiring elastomers with unprecedented mechanical performance.