Nonlinear material behaviour of spider silk yields robust webs

Abstract

Natural materials are renowned for their exquisite designs that optimize function, as illustrated by the elasticity of blood vessels, the toughness of bone and the protection offered by nacre 1,2,3,4,5 . Particularly intriguing are spider silks, with studies having explored properties ranging from their protein sequence 6 to the geometry of a web 7 . This highly adapted material system 8 , which is wellknown to meet a spider's many needs, exhibits exemplary mechanical properties 9,10,11,12,13,14,15 . It thus comes as no surprise that there has been much interest in the molecular design underpinning the outstanding performance of silk fibres 1,6,10,13,19,20 , and in the mechanical characteristics of web-like structures 16,17,18,21 . Yet it remains unknown how the mechanical characteristics of spider silk contribute to the integrity and performance of a spider web. Here we report web deformation experiments and simulations that identify the nonlinear response of silk threads to stress-involving softening at a yield point and dramatic stiffening at large strain until failure-as crucial for localizing the load-induced deformation and hence for endowing spider webs with robustness. Control simulations confirm that a nonlinear stress response results in superior resistance to defects compared to linear elastic or elastic-plastic (softening) material behaviour. We further show that under distributed loads, such as exerted by wind, the behaviour of silk under small-deformation is essential in maintaining the web's structural integrity. The superior performance of silk in webs is therefore not merely due to its exceptional ultimate strength and strain, but more importantly arises from the nonlinear response of silk threads to strain and their geometrical arrangement in a web.While spider silk is employed in a myriad of functions from wrapping prey to lining retreats 22,23 , here we focus on silk's structural role in aerial webs and on how silk's material properties relate to web function. The mechanical behaviour of silk, like that of other biological materials, is determined by the nature of its constituent molecules and their hierarchical assembly into fibres 13,19,20,24,25,26 (Fig. S1). Spider webs themselves are characterized by a highly organized geometry that optimizes their function 7,8,16,17,18 . To explore the contribution of the material characteristics to web function, we develop a web model with spiral and radial threads based on the geometry commonly found in orb webs 1 . The silk material behaviour is parameterized from atomistic simulations of dragline silk from the species Nephila clavipes (Model A) 19,20 ( Fig. 1a-b) and validated against experiments 10 (Methods Summary). As properties of silk can vary across evolutionary lineages by over 100% 9,27,28 (SI Section S1), we avoid species-specific silk properties and use instead a representative model to reflect the characteristic nonlinear stress-strain behaviour of silk found in a web. The mechanical performance of individual silk threads has been...

A Materiomics Approach to Spider Silk: Protein Molecules to Webs

“…18 The starting configuration in simulations of the composite protein structure consists of a lattice of an antiparallel arrangement in one direction and a parallel arrangement in the other, based on previous Structure and geometry of fibers are visible through SEM imaging, for example 32 Spider web (cm and larger) Spider web geometry and material composition determine the deformation mechanisms of the web, responsible for optimized prey capture mechanisms Localization of failure due to a combined yielding-stiffening behavior at deformation. 35 In situ experiments conducted on garden webs showing a very similar result. 35 Geometry in model obtained from natural orb-web 35,36 findings and mimicking the natural silk spinning process that involves elongational flow and alignment of protein chains due to mechanical force (Fig.…”

“…35 In situ experiments conducted on garden webs showing a very similar result. 35 Geometry in model obtained from natural orb-web 35,36 findings and mimicking the natural silk spinning process that involves elongational flow and alignment of protein chains due to mechanical force (Fig. 1b).…”

“…6,17 (b) A summary of the multiscale approach considered here for web analysis, to link the molecular to the macroscale. 35 Silk protein structure, based on the information about its genetic makeup, is identified with methods such as replica exchange molecular dynamics and characterized to define a constitutive behavior. The molecularly derived behavior is incorporated into a macroscale web system.…”

“…The final, overarching hierarchical level we consider is a spider web model that describes silk fibers as a coarse-grained collection of beads assembled in a typical web geometry, 35 where the material behavior is derived directly from atomistic simulation of the protein composite as reviewed above (Fig. 6).…”

“…We justify this choice by noting that atomistically derived material behavior compares well with empirical studies of silk threads. 32 The web is modeled by an arithmetic spiral, 35 with radial threads extending from the center for support. The architecture and geometry are borrowed from the natural orb-web design, 36 as illustrated in Fig.…”