Zhigang Suo

Xylem pit membranes are discrete regions of primary cell wall that are permeable to water but prevent the spread of air embolism. Here we investigate how pectin, a cell wall hydrogel with a kPa-scale modulus, affects the functioning of intervessel pit membranes in Acer rubrum (red maple). We show that enzymatically digesting pectin significantly lowers the resistance against embolism spread, confirming earlier reports in other species and providing evidence that pectin is present in at least some portions of A. rubrum's intervessel pit membranes. Removing calcium with a chelating agent had a smaller effect that became non-significant after accounting for radial flows. Vulnerability curves of control and calcium removal stems measured with and without the addition of a surfactant (0.1% w/v Triton-X) exhibited large differences in P50 as expected for the change in surface tension and implying an invariant effective Laplace radius. In contrast, pectin removal stems did not exhibit a significant change in P50 when vulnerability curves were measured with and without surfactant. Instead, the difference in surface tension implied large changes in the effective Laplace radius with increasing xylem tension, suggesting that pectin removal increases the local compliance of pit membranes. We hypothesize that pectin stabilizes the spacing of cellulose microfibrils, thereby contributing to the transport of water under tension.

Natural rubber outperforms synthetic rubbers because of its long chains and strain-induced crystallization (SIC). However, these advantages are largely lost when the natural rubber chains are masticated during processing, and silica particles are added for reinforcement. Mastication eases mixing but shortens chains and lowers performance. Silica particles require covalent interlinks with rubber chains, but these interlinks restrict chain stretch and alignment, reducing SIC. Here, we show that the performance of silica-reinforced natural rubber can be markedly enhanced by preserving long natural rubber chains. We use a solvent to dissolve natural rubber latex into individual rubber chains and use the solution to uniformly disperse silica particles. After drying, the uncured compound can be stored and molded prior to curing. The long rubber chains are then sparsely crosslinked with one another and interlinked with the silica particles. The long strands readily align under stretch and increase SIC. Preserving long chains elevates toughness by an order of magnitude, from ~2 to 44 kJ m –2 . High toughness arises from energy dissipation across multiple length scales, over long rubber strands, silica particles, and a zone of SIC. High modulus of ~19 MPa arises from two interpenetrating networks: the network of densely entangled rubber chains and the network of percolated silica particles. The resulting material achieves high toughness while maintaining high modulus, a combination uncommon in silica-reinforced synthetic and natural rubbers.

A material tears, peels, and breaks by growing a crack. In a zone around the crack front, atoms undergo an irreversible process of breaking─and possibly reforming─bonds. Trailing behind the crack front are two layers of scars. Outside the irreversible zone and scars, atoms undergo the reversible process of elasticity. The irreversible zone is considered localized if it is small relative to the body. The idealization of localized irreversibility leads to a thermodynamic framework centered on the energy release rate. This crack driving force is defined using an ideal body in which a crack is stationary and deformation is elastic, and is applied to a real body in which a crack grows by an irreversible process. The irreversible zone scales with a material length: the fractocohesive length. We review recent advances in the development of crack-resistant elastomers and hydrogels as well as polymer networks reinforced by hard particles, fibers, or fabrics, subject to monotonic, cyclic, and static loading. Emphasis is placed on how molecular features, such as strand length, entanglements, noncovalent bonds, and chemical reactions, govern crack resistance. Design principles are highlighted that reconcile high toughness with low hysteresis through stress deconcentration. This review traces crack resistance to molecular origins, providing a foundation for designing next-generation crack-resistant materials.

, while maintaining modulus. High toughness arises from energy dissipation across multiple length scales: along long rubber strands, across carbon particles, and in a zone of strain-induced crystallization and interfacial dissipation. Modulus is maintained through entanglements of rubber strands and percolation of carbon particles.

Plants responding to excessive soil salinity by discharging brine onto their leaf surface risk dehydration through the osmotic continuity between the living tissue and the surface brine, which further enriches with evaporation. Cuticle cracks have long been identified as essential for salt to reach the leaf surface but enable a potentially desiccating continuity between the brine and the gland interior. Using the secreting salt gland of Nolana mollis as a model system, we integrate mathematical modeling, imaging, and physiological measurements to examine the mechanical and biochemical processes required for efficient salt removal. We find that the subcuticular space between the concentrated surface brine and the more dilute secreting cell eases the energetic limits of active salt secretion by reducing the concentration gradient of salt across the cell membrane. We show that crack size plays a critical role in balancing the osmotic and pressure gradients required for salt removal without runaway foliar desiccation.

Bovine pericardium is the tissue of choice for replacing heart valves of human patients in minimally invasive surgery. The tissue has an extraordinarily high toughness of ~100 kilojoules per square meter. Here, we investigate the origin of the toughness through mechanical tests and microscopic observations. In the tissue, crimped, long, strong collagen fibers are embedded in a soft matrix. As a crack grows in the matrix, the fibers decrimp, reorient, slip, and bridge the crack. These microscopic processes enable the fibers to transmit high tension over a long distance. Using two types of experiments, we measure the bridging traction as a function of crack separation, σ(δ). The peak traction is σ 0 ~ 60 megapascals. The maximum separation is δ 0 ~ 6 millimeters, two to four orders of magnitude higher than that of hard tissues. Both the high traction and large separation of the bovine pericardium contribute to its high toughness.

Polymers crosslinked by covalent bonds suffer from a conflict: dense covalent crosslinks increase modulus but decrease fatigue threshold. Polymers crosslinked by physical bonds commonly have large hysteresis. Here we simultaneously achieve high modulus, high fatigue threshold, and low hysteresis in a network of unusually long polymer chains crosslinked by domains of physical bonds. When the network without precrack is pulled by a moderate stress, chains in the domains slip negligibly, so that the domains function like hard particles, leading to high modulus and low hysteresis. When the network with a precrack is stretched, the chains in the domains at the crack tip slip but do not pull out. This enables high tension to transmit over long segments of chains, leading to a high fatigue threshold. Crosslinked polymers often suffer from increased modulus with decreased fatigue threshold or large hysteresis. Here the authors achieve high modulus, high fatigue threshold, and low hysteresis in a network of unusually long polymer chains crosslinked by domains of physical bonds.

When a material is cyclically loaded, an amplitude of load exists, called the threshold, below which a crack does not grow. In a polymeric material, physical interactions between polymer chains are much weaker than covalent bonds between repeat units along an individual chain. Consequently, when a crack impinges on a chain, high tension transmits along a long length of the chain. Breaking a single covalent bond dissipates the energy stored in that long length. The longer the length over which high tension transmits, the higher the threshold. Here we review how stress deconcentrates in diverse polymeric materials, including polymer networks, particle-reinforced elastomers, glassy polymers, semicrystalline polymers, phase-separated polymers, and composites. Ample opportunities exist for investigation and innovation.

ABSTRACT Plants responding to excessive soil salinity by discharging brine onto their leaf surface risk dehydration through the osmotic continuity between the living tissue and the surface brine, which further enriches with evaporation. Cuticle cracks have long been identified as essential for salt to reach the leaf surface but provide the potentially desiccating continuity between the brine and the gland interior. Using the secreting salt gland of Nolana mollis as a model system, we integrate mathematical modeling, imaging, and physiological measurements to examine the mechanical and biochemical processes required for efficient desalination. We find that the subcuticular space between the concentrated surface brine and the more dilute secreting cell eases the energetic limits of active desalination by reducing the concentration gradient of salt across the cell membrane. We show that crack size plays a critical role in balancing the osmotic and pressure gradients required for salt removal without runaway foliar desiccation.

Experiments have long shown that a polymer network of covalent bonds commonly ruptures at a stress that is orders of magnitude lower than the strength of the covalent bonds. Here we investigate this large reduction in strength by coarse-grained molecular dynamics simulations. We show that the network ruptures by sequentially breaking a small fraction of bonds, and that each broken bond lies on the minimum "shortest path". The shortest path is the path of the fewest bonds that connect two monomers at the opposite ends of the network. As the network is stretched, the minimum shortest path straightens and bears high tension set by covalent bonds, while most strands off the path deform by entropic elasticity. After a bond on the minimum shortest path breaks, the process repeats for the next minimum shortest path. As the network is stretched and bonds are broken, the scatter in lengths of the shortest paths first narrows, causing stress to rise, and then broadens, causing stress to decline. This sequential breaking of a small fraction of bonds causes the network to rupture at a stress that is orders of magnitude below the strength of the covalent bonds.

We investigate fatigue crack growth in a polymer glass in which polymer chains are long and not crosslinked. Atoms bind by forces of two types: covalent bonds between repeat units along a chain, which resist chain scission, and noncovalent interactions between the chains, which resist chain slip. The covalent bonds are much stronger than the noncovalent interactions. When a crack impinges on a long chain, the chain slips and transmits tension over a segment of the chain. When the chain breaks at a single covalent bond, the energy stored in the segment dissipates. This molecular picture suggests a hypothesis: the fatigue threshold increases as the yield strength decreases. We analyze this hypothesis by developing a shear-lag model. We test the hypothesis by using high-molecular-weight poly(methyl methacrylate), and by modifying noncovalent interactions with plasticizers.

Many composites consist of matrices of elastomers and nanoparticles of stiff materials. Such composites often have superior properties and are widely used. Embedding elastomers with nanoparticles commonly necessitates intense shear, using machines like extruders and roll millers, which cut polymer chains and degrade properties. Here, we prepare a rubber-glass nanocomposite by using two aqueous emulsions. Each emulsion is separately prepared with a single species of polymer chains. Each polymer chain is copolymerized with a small amount of silane coupling agent. Upon mixing the two emulsions, as water evaporates, the glassy particles retain the shape, and the rubbery particles change shape to form a continuous matrix. Subsequently, the silane coupling agent condensates, which cross-links the rubbery chains and interlinks the rubbery chains to the glassy particles. The cross-links and interlinks stabilize the nanostructure and lead to superior properties. The nanocomposite simultaneously achieves high modulus (~30 MPa), high toughness (~100 kJ m −2 ), and high fatigue threshold (~1,000 J m −2 ). The method of mixed emulsion is environmentally friendly and compatible with various open-air manufacturing processes, such as coat, cast, spray, print, and brush. Additionally, the silane coupling agent can interlink the nanocomposite to other materials. The method of mixed emulsion can be used to fabricate objects of complex shapes, fine features, and prescribed spatial variations of compositions.

This study focuses on the microscopic processes of crack growth in a composite of knitted fabric and soft matrix in the course direction under both monotonic and cyclic stretching.

In a hydrogen fuel cell, an electrolyte membrane conducts protons, but blocks electrons, hydrogen molecules, and oxygen molecules. The fuel cell often runs unsteadily, resulting in fluctuating water production, causing the membrane to swell and contract. The cyclic deformation can cause fatigue crack growth. This paper describes an approach to develop a fatigue-resistant polymer electrolyte membrane. The membrane is prepared by forming an interpenetrating network of a plastic electrolyte and a rubber. The former conducts protons, and the latter enhances fatigue resistance. The introduction of the rubber modestly reduces electrochemical performance, but significantly increases fatigue threshold and lifespan. Compared to pristine plastic electrolyte, Nafion, an interpenetrating network of Nafion and perfluoropolyether (PFPE) reduces the maximum power density by 20%, but increases the fatigue threshold by 175%. Under the wet/dry accelerated stress test, the fuel cell with the Nafion-PFPE membrane has a lifespan 1.7 times that of a fuel cell with the Nafion membrane.

Abstract Field concentration is often regarded as a problematic issue in soft electronics applications, especially when using curved electrodes, and in particular, those with sharp edges. However, field concentration can be turned into an advantage with appropriate device design. Herein, the applications of field concentration in hydrogel‐elastomer devices are explored. Three different types of electroluminescent hydrogel‐elastomer devices are fabricated using different types of electrodes and different light patterns. In addition, the effect of the field concentration can be extended into the bulk of the elastomer by preparing porous silicone elastomers and filling them with silicone oil. These devices are shown to be flexible and possess both good luminance and a long lifetime.

A material-specific length, called the flaw sensitivity length or fractocohesive length, is determined by measuring the strength of samples that contain cracks of various lengths. When the crack length is small compared with the fractocohesive length, the strength is unaffected by the crack. When the crack length is large compared with the fractocohesive length, the strength reduces as the crack length increases. Here we study how the fractocohesive length is affected by the stochastics of the constituents of a material. We simulate a model system, a truss in which the constituents are linearly elastic members forming a geometrically periodic lattice. The stochastics are represented by the scatter of strength among the members. The fractocohesive length scales with the length of each individual member, but the prefactor increases with the degree of scatter in member strength. The fractocohesive length can be much larger than the constituents of a material when the constituents have pronounced statistical variation.

Adhesives are commonly assessed by two properties: strength and toughness. Here we study how strength and toughness are affected by adhesive thickness. We sandwich gelatin adhesives of various thicknesses between glass substrates. The transparency of the adhesives and substrates enables us to observe crack nucleation and growth. We measure strength by lap shear of samples without precrack, and measure toughness by lap shear of samples with precrack. Our data show a characteristic adhesive thickness, about 0.5 mm. For adhesives below the characteristic thickness, strength is independent of thickness, but toughness increases with thickness. For adhesives above the characteristic thickness, strength decreases as thickness increases, but toughness is a constant. Strength scatters narrowly for samples of a thin adhesive, but broadly for samples of a thick adhesive. By contrast, toughness scatters narrowly for samples of all thicknesses. This work shows the importance of assessing adhesives of various thicknesses.

In this research, the attenuation characteristics of skid resistance of Yangyan Road was investigated by on-site test and laboratory loading system. Firstly, by employing the Dynamic Friction Tester, the skid resistance of Yangyan road in Beijing for three years were tested to anlyze its attenuation characteristics of skid resistance. Secondly, its service process was simulated in the laboratory by the one-third scale Model Mobile Load Simulator (MMLS3), while conducting the skid resistance test for the corresponding service time of on-site anti-skidding test to compare attenuation characteristics between the laboratory and on-site skid resistance. The research results showed that the skid resistance of Yangyan Road presented a logarithmic function attenuation trend with the increase of service time. The skid resistance of the asphalt mixture slightly increased to the peak value during the three months of the simulated service period, before presenting a logarithmic function attenuation trend. The attenuation rate of the skid resistance in the laboratory test was significantly smaller than that of on-site test due to effects of environmental factors on the actual roads during their service.

Hydrogels are being developed to bear loads. Applications include artificial tendons and muscles, which require high strength to bear loads and low hysteresis to reduce energy loss. However, simultaneously achieving high strength and low hysteresis has been challenging. This challenge is met here by synthesizing hydrogels of arrested phase separation. Such a hydrogel has interpenetrating hydrophilic and hydrophobic networks, which separate into a water-rich phase and a water-poor phase. The two phases arrest at the microscale. The soft hydrophilic phase deconcentrates stress in the strong hydrophobic phase, leading to high strength. The two phases are elastic and adhere through topological entanglements, leading to low hysteresis. For example, a hydrogel of 76 weight % water, made of poly(ethyl acrylate) and poly(acrylic acid), achieves a tensile strength of 6.9 megapascals and a hysteresis of 16.6%. This combination of properties has not been realized among previously existing hydrogels.

ABSTRACT Corners concentrate elastic fields and often initiate fracture. For small deformations, it is well established that the elastic field around a corner is power-law singular. For large deformations, we show here that the elastic field around a corner is concentrated but bounded. We conduct computation and an experiment on the lap shear of a highly stretchable material. A rectangular sample was sandwiched between two rigid substrates, and the edges of the stretchable material met the substrates at 90° corners. The substrates were pulled to shear the sample. We computed the large-deformation elastic field by assuming several models of elasticity. The theory of elasticity has no length scale, and lap shear is characterized by a single length, the thickness of the sample. Consequently, the field in the sample was independent of any length once the spatial coordinates were normalized by the thickness. We then lap sheared samples of a polyacrylamide hydrogel of various thicknesses. For all samples, fracture initiated from corners, at a load independent of thickness. These experimental findings agree with the computational prediction that large-deformation elastic fields at corners are concentrated but bounded.

provides agencies with more incentive to impose short-term costs to obtain longterm benefits such as environmental and health improvements.Much has changed since 2003.Real returns to US Treasury notes-a common measure of the risk-free consumption rate-have trended lower, reflecting deep structural changes in the economy (4, 5).Recent economic literature strongly supports the use of a consumption discount rate over a capital rate of return over longer time horizons (6, 7) and shows that lower discount rates are appropriate for valuing long-term effects (8, 9).Consistent with these principles, the US Office of Management and Budget's (OMB's) proposed update (1) uses more recent economic data to lower the consumption-based discount rate from 3% to close to 2%.It also ends the use of the 7% discount rate in regulatory analysis, replacing capitalbased discount rates with a shadow price of capital approach that bounds the potential impacts of public interventions on capital (10).In addition, the update calls for a Ramsey framework that links discounting to economic growth and a declining rate over longer time horizons (11).OMB could improve its update further by improving its discussion of risk.The draft focuses on risk-free discount rates and recommends modeling the insurance value of a policy with uncertain net benefits using certainty-equivalents (9).However, agencies may lack sufficient expertise to make such calculations.OMB should offer additional guidance on how to convert cash flows to certainty-equivalents, including how to specify preference parameters consistent with the risk-free rate (11).To ease agency burden, OMB should provide an approximation of the average social risk premium adjustment 26

A polymer network fractures by breaking covalent bonds, but the experimentally measured strength of the polymer network is orders of magnitude lower than the strength of covalent bonds. We investigate the effect of statistical variation of the number of links in polymer chains on strength using a parallel chain model. Each polymer chain is represented by a freely-jointed chain, with a characteristic J-shaped force-extension curve. The chain carries entropic forces for most of the extension and carries covalent forces only for a narrow range of extension. The entropic forces are orders of magnitude lower than the covalent forces. Chains with a statistical distribution of the number of links per chain are pulled between two rigid parallel plates. Chains with fewer links attain covalent forces and rupture at smaller extensions, while chains with more links still carry entropic forces. We compute the applied force on the rigid plates as a function of extension and define the strength of the parallel chain model by the maximum force divided by the total number of chains. With the J-shaped force-extension curve of each chain, even a small scatter in the number of links per chain greatly reduces the strength of the parallel chain model. We further show that the strength of the parallel chain model relates to the scatter in the number of links per chain according to a power law.

A polymer network fractures by breaking covalent bonds, but the experimentally measured strength of the polymer network is orders of magnitude lower than the strength of covalent bonds. We investigate the effect of statistical variation of the number of links in polymer chains on strength using a parallel chain model. Each polymer chain is represented by a freely-jointed chain, with a characteristic J-shaped force-extension curve. The chain carries entropic forces for most of the extension and carries covalent forces only for a narrow range of extension. The entropic forces are orders of magnitude lower than the covalent forces. Chains with a statistical distribution of the number of links per chain are pulled between two rigid parallel plates. Chains with fewer links attain covalent forces and rupture at smaller extensions, while chains with more links still carry entropic forces. We compute the applied force on the rigid plates as a function of extension and define the strength of the parallel chain model by the maximum force divided by the total number of chains. With the J-shaped force-extension curve of each chain, even a small scatter in the number of links per chain greatly reduces the strength of the parallel chain model. We further show that the strength of the parallel chain model relates to the scatter in the number of links per chain according to a power law.