Robust substrate anchorages of silk lines with extensible nano -fibres Jonas O. Wolff1a Daniele Liprandi2a Federico Bosia3 Anna -Christin Joel4 and Nicola

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Robust substrate anchorages of silk lines with

extensible nano-fibres

Jonas O. Wolff1*,a, Daniele Liprandi2,a, Federico Bosia3, Anna-Christin Joel4, and Nicola

M. Pugno2,5,**

1 Department of Biological Sciences, Macquarie University, Sydney, NSW 2109, Australia

2 Laboratory of Bio-inspired, Bionic, Nano, Meta Materials & Mechanics, Department of Civil, Environmental

and Mechanical Engineering, University of Trento, Via Mesiano 77, I-38123 Trento, Italy

3 Department of Applied Science and Technology, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129,

Torino, Italy

4 Institute of Biology II, RWTH Aachen University, Worringerweg 3, 52074 Aachen

5 School of Engineering and Materials Science, Queen Mary University, Mile End Rd, London E1 4NS, UK

* corresponding author: jonas.wolff@mq.edu.au

** corresponding author: nicola.pugno@unitn.it

a These authors contributed equally to this work.

Abstract

Living systems are built of multiscale-composites: materials formed of components with

different properties that are assembled in complex micro- and nano-structures. Such biological

multiscale-composites often show outstanding physical properties that are unachieved by

artificial materials. A major scientific goal is thus to understand the assembly processes and the

relationship between structure and function in order to reproduce them in a new generation of

biomimetic high-performance materials. Here, we tested how the assembly of spider silk nano-

fibres (i.e. glue coated 0.5μm thick fibres produced by so-called piriform glands) into different

micro-structures correlates with mechanical performance by empirically and numerically

exploring the mechanical behaviour of line anchors in an orb weaver, a hunting spider and two

ancient web builders. We demonstrate that the anchors of orb weavers exhibit outstanding

mechanical robustness with minimal material use by the indirect attachment of the silk line to

the substrate through a soft domain (‘bridge’). This principle can be used to design new artificial

high-performance attachment systems.

Keywords

Spider silk; spider web; attachment; bioadhesive; structural adhesives; biomimetics

1. Introduction

The materials that living systems are built of and produce often display mechanical

properties that outperform most man-made materials. This is largely attributed to the specific

nano- and micro-composite structure of such materials: by the combination of components with

distinct properties and their specific spatial arrangement, the resulting material exhibits a mix

of characteristics that is usually not possible to achieve with independent phases or

homogeneous (and isotropic) bulk materials (1). Biological composites are also common

among adhesive secretions and organs used by organisms to achieve substrate attachment, such

as in spider silk anchors (2), mussel byssus threads (3) and gecko feet (4). This is in contrast to

artificial adhesive joints that are usually based on homogeneous bulk materials. A better

understanding of the structure-function relationships in biological structured adhesives could

inspire a new generation of adhesive systems and fasteners with previously unachieved

properties (5, 6).

Spider web anchors are micro-structures that serve as attachments for silk lines. Unlike

most other biological composite structures and materials, such as bone, nacre or wood, these

micro-structures are rapidly formed by the instant spinning of fibres from a secretion stock and

their behavioural assembly into distinct architectures. As the fibre arrangement affects the

mechanical properties of the structure, a spider can tailor the end-product for different needs

using the same base material (7). These features make spider silk anchors very interesting for

the bio-inspiration to design instant attachments with tailored properties. However, a successful

implementation into a bio-inspired design is still hindered by a limited understanding of the

functional role of the material mix and spatial distribution of mechanical properties in silk

anchorages.

Silk anchors attach a structural thread, the dragline, to the substrate by a plaque

(membrane) that is composed of numerous adhesive nano-fibres (diameter ~0.5 μm). The base

material of the plaque is the so-called piriform silk. Tensile stress tests of this special type of

silk have revealed that it is three times more extensible than the common dragline silk (major

ampullate silk) (8, 9).

Previous research has shown that the morphology of spider web anchors can be

approximated as a tape-like membrane with the dragline fused along the central axis (10). The

location where the dragline exits the membrane (‘loading point’) thereby affects the maximal

force the anchor can sustain under tensile load (10). If the dragline is stressed, the membrane is

locally deformed and detaches from the substrate surface, along what is referred to as “peeling

line”. Membrane delamination thus leads to a changing -often growing- peeling line. After

Kendall’s peeling theory (11) the peeling force of elastic films emerges as proportional to the

length of the peeling line. It can be empirically observed, that if the anchor loading point is

close to the membrane edge, the peeling line is roughly V-shaped, whereas it is concentric when

the loading point is in a central position developing a larger length before meeting the

membrane edge (10). Previous comparative measurements and numerical simulations

uncovered that dragline placement modulates the anchor’s strength, with the ‘centrality’ of the

dragline joint cd (i.e. the distance between the loading point and the front edge of the anchor

membrane divided by the membrane length) being the main determinant of anchor performance

within species (10, 12).

It remains uncertain how the differences in mechanical properties of the attachment silk

and the dragline affect anchor strength, and if there is an optimal ratio of extensible and stiff

materials combined in the anchorage. Also, explorative studies have shown that the structure

of the dragline joint differs between species, with the dragline being either directly embedded

in the piriform silk film in some or suspended in a flexible network of piriform fibres (called

‘bridge’) in others (13) (Fig. 1). The bridge is built of the same material as the silk film applied

to the substrate (the plaque). However, while in the plaque the piriform fibres are arranged in a

lattice-like structure, they form a radial network of branching bundles in the bridge (Figs. 1h,

p). This may reduce stress concentrations in the loading point and enhance anchor resistance at

steep pulling angles. A previous in-depth study on the anchorages of the golden orb weaver

Trichonephila plumipes revealed that the bridge was asymmetric with a stronger expression in

the upstream (i.e. the leaving) dragline insertion (10). When pulling on the upstream dragline,

a higher force was required to detach the anchor from a polymer surface than when pulling on

the downstream dragline, were the bridge was much smaller (10). Therefore, we hypothesized

that the bridge enhances the overall robustness of the anchorage. To test this conjecture, we

combined an empirical and a numerical study of anchor detachment mechanics in four species

that differ in the structure of the dragline joint.

2. Results

2.1. Effects of structure on silk anchor mechanics

For the comparative analysis of anchor mechanics, four species were chosen that

differed in their silk ecology and silk anchor structure. The Southern house spider Kukulcania

hibernalis (Fig. 1a) and the Tasmanian cave spider Hickmania troglodytes (Fig. 1b) are ancient

sheet web builders that barely changed over a long evolutionary timescale. Both species build

sheet webs, but while in K. hibernalis the sheet is placed directly on the substrate surface, the

sheet of H. troglodytes is horizontally suspended between rocks which may mechanically be

more demanding. The huntsman Isopeda villosa (Fig. 1c) is an arboreal hunting spider that uses

dragline to secure itself but does not build webs for prey capture. The golden orb weaver

Trichonephila plumipes (Fig. 1d) is a large aerial web builder and represents the most advanced

silk use.

We found that in K. hibernalis the dragline was directly incorporated into the membrane,

with single strands separately following the looping patterns of the piriform silk fibres (Figs.

1e, j, r). In the three other species, the dragline fibres were bundled and did not follow the

looping patterns of piriform silk fibres in the membrane but were oriented along the middle axis

of the more or less axial-symmetrical membrane. While the dragline bundle was attached on

top of the membrane in H. troglodytes (Figs. 1f, l, s), it was suspended in a radial network of

piriform fibre bundles (called piriform silk ‘bridge’) in T. plumipes (Figs. 1h, p, u; see also 3D-

reconstruction and sections in Wolff & Herberstein (10)). A piriform silk bridge was also

present in I. villosa, but to a lesser extend (Figs. 1g, n, t).

We compared the nominal anchor strength Fmax/A of the anchors of the four species as

the maximal pull off force divided by the plaque area, by pulling off the samples

perpendicularly from a (here polypropylene) surface. Nominal strength differed between all

species (K. hibernalis – H. troglodytes: p=0.037; K. hibernalis – I. villosa: p<0.001; K.

hibernalis – T. plumipes: p<0.001; H. troglodytes – I. villosa: p=0.030; H. troglodytes – T.

plumipes: p<0.001; I. villosa – T. plumipes: p=0.015). It was higher in anchors with a bridge

than in those without a bridge. Anchors of T. plumipes yielded a ten times higher strength than

the anchors of K. hibernalis, on average (Fig. 2a). We further analysed the relationship between

cd and Fmax. Due to the intraspecific variation of silk anchors, we could obtain and measure

samples covering a range of cd values. In all species, Fmax was a clear function of cd (K.

hibernalis: R² = 0.554, p = 0.006; H. troglodytes: R² = 0.550, p = 0.001; I. villosa: R² = 0.576,

p < 0.001; T. plumipes: R² = 0.624, p < 0.001). However, assuming a linear relation Fmax/A=a



cd,

slopes varied between species from low in K. hibernalis (a = 6.97 mN/mm2) to steep in T.

plumipes (a = 34.28 mN/mm2) (Fig. 2b).

In addition to perpendicular (θ = 90°) pull-off tests, we performed similar tests at θ = 0°

(i.e. along the dragline, parallel to the substrate) and θ = 180° (dragline flipped over) in all

species except K. hibernalis. We found that Fmax was highest at θ = 0° in all species. However,

the reduction of anchor resistance at θ = 90° and θ = 180° differed between species (Figs. 3b,

d, f). Notably, Fmax was negatively proportional to the pull-off angle in H. troglodytes (0° vs.

90°: p<0.001; 0° vs. 180°: p<0.001; 90° vs. 180°: p=0.909) (Figs. 3a, b), while force drops were

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Robustsubstrateanchoragesofsilklineswithextensiblenano-fibresJonasO.Wolff1*,a,DanieleLiprandi2,a,FedericoBosia3,Anna-ChristinJoel4,andNicolaM.Pugno2,5,**1DepartmentofBiologicalSciences,MacquarieUniversity,Sydney,NSW2109,Australia2LaboratoryofBio-inspired,Bionic,Nano,MetaMaterials&Mechanics,Departmen...

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Robust substrate anchorages of silk lines with extensible nano -fibres Jonas O. Wolff1a Daniele Liprandi2a Federico Bosia3 Anna -Christin Joel4 and Nicola

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