Living tissues show an extraordinary adaptiveness to strain, which is crucial for their proper biological functioning 1,2 . The physical origin of this mechanical behaviour has been widely investigated using reconstituted networks of collagen fibres, the principal load-bearing component of tissues 3,4,5 . However, collagen fibres in tissues are embedded in a soft hydrated polysaccharide matrix which generates substantial internal stresses whose effect on tissue mechanics is unknown 6,7,8 . Here, by combining mechanical measurements and computer Stress management in composite biopolymer networksAdditional Information

Collagen forms the structural scaffold of connective tissues in all mammals. Tissues are remarkably resistant against mechanical deformations because collagen molecules hierarchically self-assemble in fibrous networks that stiffen with increasing strain. Nevertheless, collagen networks do fracture when tissues are overloaded or subject to pathological conditions such as aneurysms. Prior studies of the role of collagen in tissue fracture have mainly focused on tendons, which contain highly aligned bundles of collagen. By contrast, little is known about fracture of the orientationally more disordered collagen networks present in many other tissues such as skin and cartilage. Here, we combine shear rheology of reconstituted collagen networks with computer simulations to investigate the primary determinants of fracture in disordered collagen networks. We show that the fracture strain is controlled by the coordination number of the network junctions, with less connected networks fracturing at larger strains. The hierarchical structure of collagen fine-tunes the fracture strain by providing structural plasticity at the network and fiber level. Our findings imply that low connectivity and plasticity provide protective mechanisms against network fracture that can optimize the strength of biological tissues.

By performing extensive simulations with unprecedentedly large system sizes, we unveil how rigidity influences the fracture of disordered materials. The largest damage is observed close to rigidity points when the rupture thresholds are small. Fewer bonds are broken when the thresholds are increased. Irrespectively of network and spring properties, a more brittle fracture is observed upon increasing system size, even in sub-isostatic networks where the underlying force chains govern the mechanical response. Most of the fracture descriptors show power-law size-scaling dependent on rigidity properties. Strikingly, the maximum stress drop, a proxy for brittleness, displays a universal doubly-non-monotonic dependence on system size and can be used as a novel parameter to identify different failure regimes. Our results indicate how to tune these regimes. Finally, we speculate how the size-induced brittleness is influenced by thermal fluctuations. arXiv:1907.11466v1 [cond-mat.soft]

The dynamics of interstitial dopants govern the properties of a wide variety of doped crystalline materials. To describe the hopping dynamics of such interstitial impurities, classical approaches often assume that dopant particles do not interact and travel through a static potential energy landscape. Here we show, using computer simulations, how these assumptions and the resulting predictions from classical Eyring-type theories break down in entropically stabilized body-centered cubic (BCC) crystals due to the thermal excitations of the crystalline matrix. Deviations are particularly severe close to melting where the lattice becomes weak and dopant dynamics exhibit strongly localized and heterogeneous dynamics. We attribute these anomalies to the failure of both assumptions underlying the classical description: (i) The instantaneous potential field experienced by dopants becomes largely disordered due to thermal fluctuations and (ii) elastic interactions cause strong dopant-dopant interactions even at low doping fractions. These results illustrate how describing nonclassical dopant dynamics requires taking the effective disordered potential energy landscape of strongly excited crystals and dopantdopant interactions into account.anomalous dynamics | doping | crystals D oping pure crystalline solids with small amounts of interstitial impurities is a widely used method to enhance material properties such as heat and electric conductivity (1-4) or to tailor mechanical properties (5). Prototypical examples include the introduction of carbon atoms in iron crystals to make steel or the doping of plastic crystals with Li ions to create solid-state batteries (4). To ensure longevity of doped materials, it is essential that the spatial homogeneity and transport dynamics of the dopants within the crystal are well controlled and understood. Although theories and models are abundant (5-11), it remains unclear how large thermal excitations of the matrix lattice affect the dynamics of dopants. This becomes of particular interest during the processing of doped crystals, where they are heated close to or beyond their melting point. For example in body-centered cubic (BCC) iron doped with carbon, significant deviations from the exponential increase of diffusivity with temperature, expected from Arrhenius' law, are observed close to the melting temperature where lattice excitations are strong (12). Whereas doping is typically performed to tailor material properties at the macroscopic scale, these enhanced properties emerge from the dynamics and interactions between dopants at the scale of individual atoms (13). In classical theories for dopant dynamics, impurity particles are described as hopping through a potential energy landscape that is set by a perfect lattice symmetry, with transition rates governed by the energy barriers between adjacent interstitial sites and their occupancy (6,7,14). In reality, thermal fluctuations of atoms away from their equilibrium lattice positions will randomize the instantaneous potential energy l...

Soft network materials exist in numerous forms ranging from polymer networks, such as elastomers, to fiber networks, such as collagen. Also 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.