Abstract
This work establishes a tensegrity model of spider dragline silk. Tensegrity systems are ubiquitous in nature, being able to capture the mechanics of biological shapes through simple and effective modes of deformation via extension and contraction. Guided by quantitative microstructural characterization via air plasma etching and low voltage scanning electron microscopy, we report that this model is able to capture experimentally observed phenomena such as the Poisson effect, tensile stress-strain response, and fibre toughness. This is achieved by accounting for spider silks’ hierarchical organization into microfibrils with radially variable properties. Each fibril is described as a chain of polypeptide tensegrity units formed by crystalline granules operating under compression, which are connected to each other by amorphous links acting under tension. Our results demonstrate, for the first time, that a radial variability in the ductility of tensegrity chains is responsible for high fibre toughness, a defining and desirable feature of spider silk. Based on this model, a discussion about the use of graded tensegrity structures for the optimal design of next-generation biomimetic fibres is presented.
Highlights
It is generally accepted that the remarkable mechanical performance of spider silk dragline originates from a hierarchical organization of proteins into a hydrogen bonded structure of ordered crystalline β-sheets, embedded in a disordered amorphous matrix [1,2,3,4,5,6]
At the mesoscale, it has been shown that silk assembles into nanofibrils with diameters ranging from ~30 nm [3] to more than 100 nm [2,5] and that a fibre has structurally and functionally distinct regions; a load bearing core (consisting of inner (1800–2300 nm), and outer (300–400 nm) sections [2,7,8]) surrounded by protective lipid (10–20 nm), glycol (40–100 nm), and skin (50–100 nm) layers [2]
Skelton and Nagase [19] have observed that a tensegrity model of a spider silk fibre that accounts for the transverse stiffening effect played by the crystalline granules leads to an increase of the overall tensile stiffness, as compared to a tendon-only model
Summary
It is generally accepted that the remarkable mechanical performance of spider silk dragline originates from a hierarchical organization of proteins into a hydrogen bonded structure of ordered crystalline β-sheets, embedded in a disordered amorphous matrix [1,2,3,4,5,6]. Skelton and Nagase [19] have observed that a tensegrity model of a spider silk fibre that accounts for the transverse stiffening effect played by the crystalline granules leads to an increase of the overall tensile stiffness, as compared to a tendon-only model. The assumed value of Eβ, which whilst significantly higher than the experimental Young’s moduli of β-sheet nanocrystals reported in the literature [33,35], is imported from the theoretical study presented in [30] It refers to the rigid response of the β-crystalline domains in the pre-yield and pre-buckling regimes in tension and compression, respectively. The current model confines the radial deformation mechanism to the inner core formed by the type 3 fibrils, whose radius is equal to 65% of the overall fibre radius (see Figure 3). We are led to conclude that the present model accurately predicts the fibre volume conservation in the large strain regime, being able to reproduce the small fluctuations of the volumetric strain experimentally observed in [12]
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