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Rubbers reinforced with rigid particles are used in high-volume applications, including tyres, dampers, belts and hoses1. Many applications require high modulus to resist excessive deformation and high fatigue threshold to resist crack growth under cyclic load. The particles are known to greatly increase modulus but not fatigue threshold. For example, adding carbon particles to natural rubber increases its modulus by one to two orders of magnitude1,2,3, but its fatigue threshold, reinforced or not, has remained approximately 100 J m−2 for decades4,5,6,7. Here we amplify the fatigue threshold of particle-reinforced rubbers by multiscale stress deconcentration. We synthesize a rubber in which highly entangled long polymers strongly adhere with rigid particles. At a crack tip, stress deconcentrates across two length scales: first through polymers and then through particles. This rubber achieves a fatigue threshold of approximately 1,000 J m−2. Mounts and grippers made of this rubber bear high loads and resist crack growth over repeated operation. Multiscale stress deconcentration expands the space of materials properties, opening doors to curtailing polymer pollution and building high-performance soft machines. 

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. 

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. 

This paperstudies a co m monly observed pheno menon:theinitiation offracturefro m cornersin a brittlesoft material. Arectangular hydrogelis prepared and glued bet weent wo plastic fil ms,such that the hydrogel meets the fil ms at 90◦ corners. When the t wo plastic fil ms are pulled, the hydrogel undergoes a shear defor mation, and the stress-strain curve is recorded until fracture initiatesfromacorner.WefindthattheshearmodulusisindependentofthethicknessHofthe hydrogel, but the shear strength scales as ~ H − 0.4. A nu merical si mulation sho ws a nonlinear elastic zone around the corner, in which the stress field varies slo wly. Ho wever, when the nonlinear elastic zone is s mall co mpared to the thickness, an annulus exists in which a singular fieldoflinearelasticityprevails.Inthisannulus,thestressfieldscales withthedistanceRfrom thecorneras ~R−0.41. Wecallthisconditionsmall-scalenonlinearelasticity. Ourresultsindicate thats mall-scale nonlinear elasticity prevails even whenthe appliedshearstrainis aslarge as 80 %. This condition explainsthe experi mentally observedscaling bet weenstrength andthickness. The c o n diti o n of s m all-s c al e n o nli n e ar el asti cit y si m pli fi es t h e c h ar a ct eri z ati o n of fr a ct ur e i niti at e d fro m corners of brittle soft materials. 

A plastic may degrade in response to a trigger. The kinetics of degradation have long been characterized by the loss of weight and strength over time. These methods of gross characterization, however, are misleading when plastic degrades heterogeneously. Here, we study heterogeneous degradation in an extreme form: the growth of a crack under the combined action of chemistry and mechanics. An applied load opens the crack, exposes the crack front to chemical attack, and causes the crack to outrun gross degradation. We studied the crack growth in polylactic acid (PLA), a polyester in which ester bonds break by hydrolysis. We cut a crack in a PLA film using scissors, tore it using an apparatus, and recorded the crack growth using a camera through a microscope. In our testing range, the crack velocity was insensitive to load but was sensitive to humidity and pH. These findings will aid the development of degradable plastics for healthcare and sustainability.