Performance of a bio-inspired spider web

Performance of a bio-inspired spider web Lingyue Zheng 1, Majid Behrooz 1, Rui Li 2, Xiaojie Wang 1 and Faramarz Gordaninejad 1 1 Composite and Intelligent Materials Laboratory, Department of Mechanical Engineering, University of Nevada, Reno, Nevada 89557, USA 2 Key Laboratory of Network Control and Intelligent Instrument of Ministry of Education, Chongqing University of Posts and Telecommunications, Chongqing 400065, China ABSTRACT The goal of this study is to investigate dynamic properties and the total energy change of a bio-inspired spider web. To better understand the relationship between such capabilities, the effects of preload, radial and spiral string stiffness and damping ratio on the natural frequency and total energy of the web are numerically examined. Different types of webs materials and configurations such as damaged webs are investigated. It is demonstrated that the pretension, stiffness and damping ratio of the web s strings can significantly affect the natural frequency and total energy of the full and damaged webs. In addition, it is shown that by increasing the pretension in the radial strings one can compensate for the damaged strings of the artificial spider web. Keywords: Artificial spider web, modal analysis, total energy, damage performance 1. INTRODUCTION Spider webs have extraordinary performance even when they are damaged by wind or other insects. Spiders can redesign their webs based on the prey size, environmental circumstances, and the extent of the damage in their webs. Aoyanagi et al. 1 proposed a simple spider web model and found that the web is free of stress concentrations even when some spiral silks are broken. Lin et al. 2 addressed the characteristics of a spider web and developed a model for a real spider web. Naftilan 3 treated the web as a stretched membrane to obtain the transmission velocities of a spider web. Lin and Sobek 4 used a phenomenological model to investigate force flows through webs. 4 It is established that the spider s web energy exhaust is a results of a unique spider web structure, high tensile strength, toughness and viscoelastic behavior of spider silks 5. Ko et al. 6 developed stress-strain relationships for spider silk under different loading conditions. Spider silks and orb webs are a co-evolution system in which fibrous biomaterials-silks are arranged in a complex design resulting from stereotypical behavioral patterns, to produce effective energy absorbing traps for flying prey 7. The damping capacity of spider silk plays a critical role in how orb webs stop flying insects 8. The comparison among stress-strain behavior of spider silk and other materials, such as, nylon and rubber have been studied in detail 9. Different researches were able to determine the relationships among web properties, internal forces, damaged tolerance, vibration transmissibility and energy exhaust of spider web. Wirth et al. 10 showed that the radial pretension changes with spider mass and spider can control the web tension to catch different prey. Alam et al. 11, 12 studied a damage tolerant design in a spider web by finite element (FE) methods where he defined stress redistribution and the effect of from a few

elements on the dynamic response of the web. The energy absorption ability of the radial silk was compared to spiral silk in a study by Sensenig et al. 13 Since spider webs have superior characteristics, various bio-inspired applications of a web-like structures have been proposed. Lanzara et al. 14 used micro-scaled electronic wires to develop macroscopic, ultra-light and flexible spider web. A parametric study was conducted to predict effects of various web parameters on the natural frequencies and normal modes of vibration of a three-dimensional cable net 15. Ding et al. 16 developed nylon-6 and poly (acrylic acid) nano-nets. In this study, a finite element model is developed to examine the effects of material properties of the radial and spiral web strings on the modal performance of an artificial spider web, as well as the energy absorption and dissipation capabilities of the web in the full (non-damaged strings) and damaged states. 2. MODELING, ANALYSIS AND RESULTS In order to better understand the relationship between natural frequency and influence on total energy versus the different mechanical properties of a spider web, several modes are made using ANSYS software. Material properties used in the FE model are listed in Table 1 8. For this study, nylon and rubber are selected as the radial and spiral strings, respectively, since they have similar material properties compared to those of a real spider silk. Dimensions of a real and the artificial spider web are also shown in Table 1 for comparison. Figure 1 shows the structure of a nylon-rubber artificial web. The artificial web is constructed of 16 nylon radial strings and 12 rubber spiral strings with the diameter of 500-800 μm. The mesh width of the model, or spacing between the spiral rubber strings, is 15mm. The key parameters that affect performance of the web are: Young s modulus, pretension force and damping ratio of strings. The comparison between a full web and a web with a radial string damaged is made to examine how the properties can be changed in a damaged web to regain the same natural frequency and total energy of the full spider web. The full and damaged spider web models are shown in Figure 2. The material properties are varied independently to study their effect on the web. In addition, the effects of radial versus spiral strings on the natural frequency and the total energy are explored. Table 1. Material properties and geometric dimensions of a real spider and a nylon - rubber artificial web 8. Young's modulus (GPa) Material Properties Yield strength (MPa) Ultimate strength (MPa) Elongation Density (kg/m 3 ) Radial silkreal 1.7-16.6 75-770 780-2189 18-70% 1.35*10 3 Spiral silk-real 0.002-0.12 15-300 160-2370 200-500% 1.33*10 3 Radial stringnylon 3 50 80 18-26% 1.13*10 3 Spiral stringrubber 0.03 8 15 500-750% 1.10*10 3 Geometric Dimensions Diameter of Number of Number of Mesh width Web area string radial string spiral string (mm) (cm (μm) ) Spider webreal 10-20 10-30 0.6-6.8 0.3-10.8 55-860 Spider webrubber and nylon 8 12 500-800 15 1017

Mesh width Spiral string - rubber Radial string - nylon Figure 1. Structure of a nylon - rubber artificial web. (a) (b) Figure 2. (a) full, and (b) one radial string damaged web. Modal analysis First, the effect of the Young s modulus of the strings on the natural frequency of the web is studied. Figure 3 shows the results for the full web with different Young s modulus for radial (r) strings and constant Young s modulus for spiral (s) strings. Figure 4 presents the results for the natural frequency of the full web with different Young s modulus for spiral strings and constant Young s modulus for radial strings. In Figures 3 and 4, Young s moduli of radial and spiral strings are changed to half and twice of its original value, respectively. It is shown that by increasing Young s modulus natural frequencies are increased. As can be seen in these

Figures, the effect of increase in Young s modulus in the radial strings is more pronounced than the increase in Young s modulus of the spiral strings. Figure 3. Natural frequency of full web with different Young s modulus on radial string. Figure 4. Natural frequency of full web with different Young s modulus on spiral string. Since the loss of strings reduces web s mass and stiffness, the natural frequencies of the spider web are changed. The purpose of comparing a full web and a one-string damaged web s performance is to assess if it is possible to change material properties of the damaged web to regain similar performance as that of the full web. Figure 5 shows results for a damaged web s natural frequency with different Young s modulus for radial strings and constant Young s modulus for spiral strings. Figure 6 shows also the natural frequency for a damaged web, but with different Young s modulus for spiral strings and constant for radial strings. By comparing Figures 5 and 6, one can see that the natural frequency of the damaged web is lower than the full web. By increasing the Young s modulus of radial or spiral strings the natural frequencies increase and approach those of the full

web. As can be seen, change in the Young s modulus of radial string has more effect on the natural frequencies than change of the spiral strings. Changing Young s modulus of spiral strings is effective on changing natural frequencies in higher modes. Figure 5. Natural frequencies of damaged web with different radial string Young s modulus. Figure 6. Natural frequencies of damaged web with different spiral string Young s modulus. Next, the effect of pretension on the natural frequencies of the full and damaged webs is. Different initial pretension of 0mN, 1mN and 2mN are applied to the radial strings of a damaged web, while the Young s moduli of strings are kept constant. As shown in Figure 7, the pretension affects all modes. Therefore, it is possible to regain the full-web performance by increasing the pretension of the damaged web s radial strings.

Figure 7. Natural frequencies of damaged web with different radial string pretension. Energy analysis The total energy is the combination of strain and kinetic energy of the spider web. An impulse force of 0.3 N is applied at the center of the web starting from 0.05s and ending at 0.2s, as shown in Figure 8. The total energy of different types of artificial webs is compared by changing Young s modulus and damping ratio. The input in Figure 8 is applied to both the full and the damaged web. Figure 8. Force input at the center of spider web. Figures 9 and 10 present the effect of changing Young modulus of the radial and spiral strings on the total energy of the damaged web. For these results the pretension is zero and damping ratio is kept constant. By comparing figure 9 and 10, one can conclude that the Young moduli for both radial and spiral strings need to be doubled to compensate for the loss of one radial string in the damaged web. Finally, the effect of damping ratio of the strings for the full and damaged web on the total energy is explored, while the Young s modulus and the pretension are kept constant. As can be seen in Figures 11 and 12, the variation in damping ratio in spiral strings affects the total energy of the spider web but changing the damping ratio of radial string shows a pronounced influence on total energy than changing the damping ratio of spiral strings.

Figure 9. Comparison between the total energies of the damaged web, with different Young s moduli for radial string with the full web. Figure 10. Comparison between the total energies of the damaged web, with different Young s moduli for spiral string with the full web.

Figure 11. Comparison between the total energies of the damaged web, with different damping ratios for radial string with the full web. Figure 12. Comparison between the total energies of the damaged web, with different damping ratios for spiral string with the full web. 3. CONCLUSIONS In this work, natural frequencies and the total energy of an artificial spider web is obtained using finite element methods. It is found that the effect of Young s modulus on the natural frequencies is more than the pretension of radial strings in strengthening the damaged web to reach at the full web performance. It is found that the total energy response for a damaged web can be compensated to the same as a full web by adjusting the Young s modulus or damping ratio of the strings. The results revealed the spider web s total energy and natural frequencies are more sensitive to changes in mechanical properties of the radial strings than spiral strings.

ACKNOWLEDGEMENTS The study is supported by the University of Nevada, Reno, the National Natural Science Foundation of China under projects 51005264, and China Scholarship Council. REFERENCES [1] Aoyanagi, Y. and Okumura, K., Simple model for the mechanics of spider webs, Phys Rev Lett, 038102, 1-4 (2010). [2] Lin, L. H., Edmonds, D. T. and Vollrath, F., Structural engineering of an orb-spider s web, Nature, 373, 146-148 (1995). [3] Naftilan, S. A., Transmission of vibrations in funnel and sheet spider webs, Int J. Biol Macromol, 24, 289-293 (1999). [4] Lin, L. H. and Sobek, I. W., Structural hierarchy in spider webs and spiderweb-type system, The Structural Engineer, 76(4), 59-64 (1998). [5] Kellya, S. P., Sensenigb, A., Lorentza, K. A. and Blackledge, T. A., Damping capacity is evolutionarily conserved in the radial silk of orb-weaving spiders, Zoology, 1(14), 233-238 (2011). [6] Ko, F. K. and Jovicic, J., Modeling of mechanical properties and structural design of spider web, Biomacromolecules 5, 780-785 (2004). [7] Sensenig, A., Agnarsson, I. and Blackledge, T. A., Behavioural and biomaterial coevolution in spider orb cebs, J. Evol Biol, 23, 1839-1856 (2010). [8] Glisovic, V., Schollmeyer, T. A., Zippelius, H. and Salditt, A. T., Mechanical properties of spider dragline silk: humidity, hysteresis, and relaxation, BioPhsy J., 93, 4425-4432 (2007). [9] Gosline, J. M., Guerette, P. A., Ortlepp, C. S. and Savage, K. N., The mechanical design of spider silks: from the fibron sequence to mechanical function, J. Exp Biol, 202, 3295-3303 (1999). [10] Wirth, E. and Barth, F. G., Forces in the spider orb web, J. Comp Physiol A., 171, 359-371 (1992). [11] Alam, M. S. and Jenkins, C. H., Damage tolerance in naturally compliant structures, Int J. Damage Mech, 14, 365-384 (2005). [12] Alam, M. S., Wahab, M.A. and Jenkins, C. H., Mechanics in naturally compliant structures, Mechanics of Materials 39, 145-160 (2007). [13] Sensenig, A., Lorentz, K. A., Kelly, S. P. and Blackledge, T. A., Spider orb webs rely on radial threads to absorb prey kinetic energy, J. R. Soc. Interface 9, 1880-1891 (2012). [14] Lanzara, G., Salowitz, N., Guo, Z. and Chang, F., A spider web - like highly expandable sensor network for multifunctional materials, Adv Mater, 22, 4643-4648 (2010). [15] Gambhir, M. L. and Batchelors, B. D., Finite element study of the free vibration of 3-D cable networks, Int J. Solids Struct, 15, 127-136 (1979). [16] Ding, B., Li, C.R., Miyauchi, Y., Kuwaki, O. and Shiratori, S., Formation of novel 2D polymer nanowebs via electrospinning formation of novel 2D polymer nanowebs via electrospinning, Nanotechnology 17, 3685-3691 (2006).