Tensegrity Modelling and the High Toughness of Spider Dragline Silk

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.

Spinning Beta Silks Requires Both pH Activation and Extensional Stress

“…Together our structural measurements spanning the nano-to-micro scales could explain these fiber's high extensibility and toughness but low strength, agreeing with recent tensegrity modeling of silk. [46] Feedstocks subjected to a medium rate of work input (0.3 to 8 J (g s) −1 ) exhibit features akin to a native B. mori silk, displaying similar internal morphology and fracture surfaces under SEM (Figure 3d), degree of alignment under polarized light and FTIR (Figure 3c,b) and similar degrees of molecular disorder (Figure 3b). The fibers show a uniform fracture surface with a crack deflection at crystalline regions combined with plastic deformation in the amorphous regions.…”

“…Together our structural measurements spanning the nano‐to‐micro scales could explain these fiber's high extensibility and toughness but low strength, agreeing with recent tensegrity modeling of silk. [ 46 ]…”

Spinning conditions affect structure and properties of Nephila spider silk

“…57 Our present study has demonstrated that it is necessary to use a range of spider silk fibers processed in different ways (e.g., by varying reeling speed), such that they have different microstructures and mechanical properties, before the behavior can be fully modeled. 64,65 It should be pointed out that this modeling is based only upon the analysis of the elastic deformation of the material, but it also provides information upon how the microstructure responds to higher levels of deformation. It is possible to speculate upon how the microstructures will affect the overall toughness of the silk fibers by considering what will happen at high levels of overall strain.…”

A Mesoscale Tensegrity Model of Spider Dragline Silk Fiber

“…The presented model generalizes the one proposed in [9] and paves the way to the optimal design of innovative biomimetic fibers with tensegrity architecture.…”

“…We now focus the attention on the response of the fibre under an isochoric longitudinal stretching deformation, which stretches the fibre up to an engineering strain , where denotes the unstretched length of the fibre, and denotes the stretched length. If we consider that the volume of the fibre remains constant under stretching, as it is written in many experimental studies (refer, e.g., to [9],[10]), the length variation along the longitudinal axis occurs in association with a radial contraction of the fibre. The radial engineering strain , where is the radius of the fibre in the unstretched configuration, and is the stretched radius, is related to the longitudinal strain through We characterise the initial elastic response of the strings forming the multiwalled model in Fig.…”