Structural optimization of 3D-printed synthetic spider webs for high strength

Abstract

Spiders spin intricate webs that serve as sophisticated prey-trapping architectures that simultaneously exhibit high strength, elasticity and graceful failure. To determine how web mechanics are controlled by their topological design and material distribution, here we create spider-web mimics composed of elastomeric filaments. Specifically, computational modelling and microscale 3D printing are combined to investigate the mechanical response of elastomeric webs under multiple loading conditions. We find the existence of an asymptotic prey size that leads to a saturated web strength. We identify pathways to design elastomeric material structures with maximum strength, low density and adaptability. We show that the loading type dictates the optimal material distribution, that is, a homogeneous distribution is better for localized loading, while stronger radial threads with weaker spiral threads is better for distributed loading. Our observations reveal that the material distribution within spider webs is dictated by the loading condition, shedding light on their observed architectural variations.

Figure 1. From natural to synthetic spider webs.

(a) Photograph of a spider web, spider and small prey. The prey (indicated by an arrow) is trapped by spiral threads at the periphery of the spider web and the spider is at the centre of the web. (b) The spider moves from the web centre to approach the prey. Despite the flaw, the web is still able to support the weight of the spider. Scale bars in a,b: 10 mm. (c) Schematic figure of the computational model of an orb web under relaxation. The web is composed of radial threads and spiral threads. (d) The radial and spiral threads of a web are printed by a 3D printer on top of the aluminium frame and the substrate. (e) The frame and the web are taken off from the substrate after curing. (f) The frame is fixed and the thread in the web is stretched by a tensile testing machine. Scale bars in d–f: 25 mm.

Figure 2. Mechanical response of synthetic webs under point loading.

(a) Simulation snapshots of the deformation of a web structure under a point stretching force F applied at the middle of a spiral thread (of 24 rings of spiral threads) with distance r=0.35R from the centre of the web, where R=50.8 mm is the radius of the inner circle of the frame. The periphery of all the radial threads is fixed from displacement. For the sake of simplicity, we use a single rigid rod as a representative shape of prey to deform the web. The displacement of the point under loading (D) is normalized by R (D_normalized=D/R). (b) Experiment snapshots with the same force and boundary conditions applied to the web made of PDMS via 3D printing with spiral thread diameter of d_s=180 μm and radial thread diameter of d_r=258 μm, identical to what is used in the numerical model. (c) The simulation (sim.) and experimental (exp.) force–displacement curves of three webs with different number of rings of spiral threads under loading. (d) Mapping the local stiffness (K) of a web (of eight rings) at small deformation both in simulation and experiment. This is obtained by deforming the middle point of several spiral threads and measuring the slope of the force–displacement curve at D_normalized=0.1, as a function of the distance from the web centre to the loading point. The local stiffness is normalized by that of the innermost spiral thread.

Figure 3. Mechanical response of synthetic webs as a function of loading size.

(a) Simulation snapshots of the deformation of a web (of 24 rings) right before failure that is caused by different number of spiral threads under loading (n). (b) F–D_normalized curves of the same web under different loading conditions for different n. Curves are obtained both from simulation and experiment. (c) Comparison of the close-up of web deformation under loading with n=1 in silico (bottom) and for the experiment (top), before (left) and after (right) failure. The stretching force only breaks the spiral thread under loading. (d) Comparison of the close-up of web deformation under loading with n=12 in silico (bottom) and in the experiment (top), before (left) and after (right) failure. The stretching force breaks the radial threads connecting the spiral threads under loading. (e) Comparison of peak force (F_peak) obtained from every F–D_normalized curve as a function of n for simulation and experiment. Each of those results is exponentially fitted according to equation (1), resulting in the function F_peak=1.0[1–exp(−n/2.6)] (N) for simulation and F_peak=0.9[1–exp(−n/2.5)] (N) for experiment result.

Figure 4. Material distribution effects on web strength.

(a) Effect of homogeneously increasing thread diameters on PDMS web strength. We take the initial structure of d_{s_0}=200 μm and d_{r_0}=250 μm and keep d_s/d_r=0.8 constant for different models with increasing diameters for both threads. The peak force is normalized by the peak force of the initial web structure (F_{peak_0}=0.3 N). Linear fitting gives F_peak/F_{peak_0}=(1.03±0.01)A/A₀ for simulation and F_peak/F_{peak_0}=(0.89±0.12)A/A₀ for experiment. (b) Close-up of the simulation snapshots of applying point force (n=1) (left), force involves four spiral threads (n=4) (middle), and homogenously distributed force (force on each section of each thread is proportional to its cross-section area) to the web (right). For the third case, considering that a web usually does not subject to wind and rain loading normal to the web surface, the web is initially tilted at an angle of ϕ=26.6° with the distributed force. (c) Different failure modes for webs with d_s²/d_r² changing from 0.1 to 10 for point loading. The web with d_s²/d_r²=0.1 ruptures at the loading point while the web having d_s²/d_r²=10 ruptures in the radial threads away from loading. (d) Comparison between simulation and experiment of F_peak/M as a function of d_s²/d_r². The peak value of 3.2 N g⁻¹ is reached at d_s/d_r=1.26. (e) Simulation result of F_peak/M for the case n=4 and homogenously distributed force. Maximum F_peak/M=8.8 N g⁻¹ is reached at d_s/d_r=0.76. No peak value is identified for homogenously distributed loading, but F_peak/M increases for decreasing d_s/d_r. At d_s/d_r→0, the maximum F_peak/M is estimated as 140 N g⁻¹ for the strength of the 12 radial threads. (f) Schematics of the optimized spider web in different conditions. d_s∼d_r is for the case of small prey and self-weight, while d_r>>d_s is necessary for large prey and rain and wind that can cause homogenously distributed force.