Elasticity, or the mechanical properties of materials in tension

Get Complete Project Material File(s) Now! »

Observation of the windlass in spider silk samples

A sample made of a single spider capture thread was first extracted from a home-grown web, as explained in section 2.2.2. The sample was then carefully deposited on the force measurement setup and exposed to high relative humidity during 15 minutes to swell up the droplets, and reach a stable stationary state. A tensile experiment is then carried out, and the force is recorded. To avoid any viscous stress build up, the test is done quasi-statically, at a speed of 12 μm s−1.. A video camera is mounted on the microscope objective and synchronized with the force measurements, simply by starting the two at the same time. The results are shown in figure 2.8. stretching, when the external force is lower than the capillary force, and thus the part of the thread located inside the drop is still under effective compression. Then the fibre begins to uncoil, giving up all the accumulated length, and creating an effective force plateau TP (region II). Finally, region I is linked to the core fibre mechanical response, which acts as a simple elastic spring. The measured Young’s
modulus of the core fibre is thus found to be 5±4 MPa, in good agreement with values reported in the literature (Omenetto and Kaplan, 2010). While the force plateau resembles the mechanical behavior of a liquid (De Gennes et al., 2004), region III resembles a purely elastic solid regime. The windlassing samples have thus the combined characteristics of liquids and solids, and may be coined liquid solid mechanical hybrids.
The shape of the force-displacement curve is related to the typical J-shape of biomaterial (Gordon, 2003), but instead of being an exponential, it is composed of three straight lines of very different slopes.
We coin the shape of the transition to the solide regime (associated with the end of the uncoiling) a Vshape curve. The close ressemblance, even if accidental, is one of the argument usually taken to involve protein unfolding (Becker et al., 2003). However, if recorded with low accuracy, the shapes resemble sufficiently to be mistaken.
It can be seen quite clearly on the insets of figure 2.8 that the capture thread is actually made of two parallel fibres running together inside the droplet. The reason of the presence of the two fibres lies in the biological concept of bilateral symmetry. Almost all silk glands within the spider abdomen come in pairs, as explained in section 1.2.1. The advantages of coiling multiple fibres will be further discussed in section 5.2. Another important parameter is the speed at which the experiment is carried. Indeed, a high tensile speed might build up viscous stresses, as well as elastic stresses, as the glue droplets are made of a visco-elastic fluid. Visco-elasticity increases with the concentration of glycoproteins, and thus decreases with relative humidity as the drops are diluted. Performing measurements at very low speed and high humidity is thus required to obtain the proper quasi-static force-displacement characterization of spider capture silk.

Biological consequences for the mighty spider

It is our understanding that the windlass mechanism has been evolved to protect the structural integrity of the web. Indeed, during buffering, for instance from the wind, local compression may occur in some capture threads. In the result of compression were sagging or global buckling, these threads would adhere to each other and annihilate the stickiness of the spider web. Thus self-tension is a necessary feature for a dense and effective trap, and largely extends the lifetime of the web.
Furthermore, the existence of the windlass mechanism allows the spider to reach extreme mechanical abilities. The windlass mechanism constitutes a thread reserve in each coil, that can extend a great deal and offer very high extensibility to the whole web, on a global scale as well as on a local scale.
This is linked to the auto-hunting electrostatic effect discussed in section 1.1 (Ortega and Dudley, 2013; Vollrath and Edmonds, 2013). The very high contrast of rigidity, from quasi-null to tens of MPa, is unique and highly contributes to the overall performance of the web, by offering a controlled combination of strength and extensibility. A regular network of radial threads (stiff and not extensible) and capture threads (soft and extensible) makes for an effective and resistant trap. The effective mechanical performances are described by the damping and fracture energy of the web, as explained below.

Additional sources of damping and fracture energy

Damping is crucial for many natural systems. For instance, damping enables trees to resist the blows of wind. Damping may be caused by the interaction of fine structures such as leaves with air, contact with other trees, root interaction with soil, and dissipation in the plant material (Spatz et al., 2007). Typically, plants achieve damping ten times more efficiently than man-made structures (De Langre, 2008). In the current literature, there are discussions as to what is the actual main source of damping of a spider web. Lin et al. (1995) proposed that aerodyamics plays a large role in web damping performance, but Aoyanagi and Okumura (2010) model web damping without taking aerodynamics into account. Sensenig et al. (2012) results may be interpreted as having the main mechanical damping in the radial threads, even though they admit to have found instances where the quasi-totality of the energy is damped in capture threads.
Though its relative importance is unclear (but acknowledged as important), the windlass mechanism provides an additional source of damping. As a reserve of length, the windlass creates the need for an increased travel length before breaking. Although the quasi-static force is small compared to forces built up in the elastic regime at high strain, the viscous stress that develops during dynamic traction may be much higher. The viscosity of the drop plays an important role here, along with the visco-elasticity of the fibre itself. The latter is the damping that occurs in the amorphous matrix of the core fibre, as explained in section 1.2.1.
Additionnally, the glycoproteins present in the capture thread droplet generate a visco-elastic behavior to the liquid coating. Visco-elasticity increases drop adhesion (see section 1.3.1), as well as fracture energy. Drop viscoelasticity is an important source of dynamic stress, especially at high impact rates.
However, this might influence the uncoiling dynamics. Our intuition is that the viscoelasticity of the droplets has been optimized to secure high damping in the very first moments of insect impact, followed by uncoiling-induced viscous damping. Optimization of viscoelasticity has already been observed for insect trapping (Dumais and Forterre, 2012; Gaume and Forterre, 2007).
Damping is also linked to dynamics of the windlass and ultimately to its efficiency, as the coiling must be faster than external buffeting. This will be quantified in section 4.7, after a detailed analysis of the windlass mechanism.

READ  Modeling organic diodes 

Realisation and characterisation of the artificial windlass

Here we present the practical realisation of a fully synthetic windlass mechanism. To do so, we used ThermoPlastic PolyUrethane (TPU) combined with silicone oil droplet. TPU and the associated process to mold it into micronic fibres is described in section 3.3.1. The Young’s modulus of these fibres is 19±3 MPa, in good agreement with the value given by the producer. The fibre size required for coilability is given in equation (1.6). The dynamic viscosity of the oil was 1000 mPa s, which allows deposition of a large and stable amount of liquid. The resulting drop-on-coilable-fibre sample is compressed below the slack length of the core fibre to induce coiling. It is indeed observed for droplets large enough (as defined in equation (1.5)) as a slight retightening of the fibre and subsequent drop lift upon coiling activation.
The fibre coiling is further observed under microscope, following the techniques given in section 2.2.2. Because of the curved liquid interfaces, the droplet is able to focus incoming light and act as a lense. As a consequence, the periphery of the drop is hard to illuminate, as explained in section 2.2.2. In contrast to natural samples, micronic fibres of TPU have the capacity to polarize incoming light. This might be due to the small size of the produced fibres with respect to the size of the polyurethane molecules.
This can induce alignment of these molecules in the main axis of the fibre and thus anisotropic interaction with light. We harvest the polarizing power of the fibres to change the light intensity of the fibre independently from the background. This is done by using two polarizers, one at the light source and one at the microscope lense. The sample will then receive polarized light. The light that goes through the fibre sees its polarization plane rotated, while the background polarization is unchanged. By crossing the two polarizers at right angle, one may “switch off” the background and reach an excellent contrast, as seen on figure 3.14. One may obtain a similar effect by simply putting the light source perpendicular to the axis of the microscope. The polarizing method has the advantage of reducing glares and enhancing edge sharpness. It is also useful to illuminate properly the part of the fibre close to the envelope of the droplet, which makes up tmost of the wetted fibre length.

Table of contents :

1 History and context of the study 
Birth of this study
1.1 Everything you always wanted to know about spiders
1.2 Silk factory, up to 7 different silks
1.2.1 Mechanical properties
1.3 Virtues of the capture thread
1.3.1 Optimized glue performance
1.4 Extreme mechanics
1.4.1 Elasticity, or the mechanical properties of materials in tension
1.4.2 Buckling mechanics
1.4.3 Surface tension
1.4.4 Elasto-capillary interactions
1.5 Critical radius of coilable fibre
2 Natural windlass 
2.1 Confusion in literature: an unsolved problem
2.2 Observation of the windlass
2.2.1 Presentation of the spiders we used
2.2.2 Materials and methods part I
2.2.3 Observation of the windlass in spider silk samples
2.3 Biological consequences for the mighty spider
2.3.1 Liquid-solid mechanical hybrid
2.3.2 Additional sources of damping and fracture energy
3 Universality of the windlass – theory, simulations and experiments 
3.1 Theory of the windlass mechanism
3.1.1 Analogy with phase transition
3.1.2 A subcritical transition
3.2 Numerical simulations of the windlass
3.3 Reproducing the natural windlass
3.3.1 Materials and methods part II
3.3.2 Realisation and characterisation of the artificial windlass
4 Fine details of the windlass 
4.1 Coiling activation
4.2 Macroscopic consequences of the existence of the meniscii
4.3 Experimental subcriticality
4.3.1 Highlights of an hysteresis
4.3.2 Force undershoot at coiling activation
4.4 What are the limits of the windlass ?
4.5 Coiling morphology and related droplet deformation
4.5.1 Different morphologies
4.5.2 Quantification of drop deformation
4.6 Effects of gravity
4.6.1 Rethinking the critical radius calculations
4.6.2 A perfectly extensible frame effect with an inextensible fibre
4.6.3 Gravity-induced hysteresis
4.6.4 Gravity-induced deactivation of the windlass
4.7 Insight into the dynamical behavior
5 Extension of the study and Conclusion 
5.1 Technological implications
5.2 Multi-fibres windlass
5.2.1 Bundle of fibres in a single droplet
5.2.2 Crossed fibres, towards a bidimensionnal windlass
5.3 On-demand activation
5.3.1 Glass transition
5.3.2 Chemical environnement change
5.4 Coiling new materials
5.4.1 Metallized TPU
5.4.2 Glass nanofibres
5.5 Macro-windlass
5.6 Microfabrication
5.6.1 Microtangles
5.6.2 Micro-coils
5.7 Conclusion
Appendix A Different kinds of capture threads 
A.1 Cribellate versus ecribellate
A.2 Wet versus dry adhesion
Appendix B A drop on a fiber 
B.1 Shape of a drop on a fiber
B.1.1 Measuring the contact angle
B.1.2 Roll-up instability
B.2 Force of a drop on a fiber
Appendix C Image processing under Mathematica and ImageJ 
C.1 Fibre diameter measurement
C.2 Fibre quality
Appendix D Material datasheets and properties 
D.1 ThermoPlastic PolyUrethane (TPU)
D.2 PolyLactic Acid (PLA)
D.3 Silicone oil from Rhodorsil
D.4 Leica microscope and optical setup
D.5 FemtoTools force sensors and SmarAct linear micro-step motor
Appendix E Gallery of fluid stagnation 
Appendix F Publications 


Related Posts