Skip to main content
Log in

Numerical simulations demonstrate that the double tapering of the spatualae of lizards and insects maximize both detachment resistance and stability

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

Many biological attachment devices of insects, spiders and geckos consist of arrays of hairs (setae), which are terminated by contact elements of different shapes. However, the most frequently observed shape is a thin plate-like spatula. In spite of a rather wide range of sizes, most spatulae of different animals are not uniform, but rather possess a gradient in thickness and width. Here we show that the spatulae of insects and geckos become gradually thinner and wider approaching the end. This geometrical effect is explained in the present paper, by using a numerical approach for the modelling of the van der Waals adhesion and friction between the contact elements and the substrate. The approach suggests that the observed negative thickness gradient contributes to the improvement of the adhesion resistance, whereas the positive width gradient increases the stability of the detachment, probably a key factor in controlling the animal walking.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aristotle (343 B.C.) Historia animalium, http://etext.virginia.edu/toc/modeng/public/AriHian.html

  • Arzt E, Gorb S, Spolenak R (2003) From micro to nano contacts in biological attachment devices. Proc Natl Acad Sci USA 100: 10603–10606

    Article  CAS  Google Scholar 

  • Autumn K (2007) Gecko adhesion: structure, function, and applications. MRS Bull 32: 473–478

    Article  Google Scholar 

  • Autumn K, Dittmore A, Santos D, Spenko M, Cutkosky M. (2006) Frictional adhesion: a new angle on gecko attachment. J Exp Biol 209: 3569–3579

    Article  CAS  Google Scholar 

  • Autumn K, Gravish N (2008) Gecko adhesion: evolutionary nanotechnology. Phil Trans Roy Soc A 366:1575–1590. http://rsta.royalsocietypublishing.org/

    Google Scholar 

  • Autumn K, Hsieh ST, Dudek DM, Chen J, Chitaphan C, Full JR (2007) Dynamics of geckos running vertically. J Exp Biol 209: 260–272

    Article  Google Scholar 

  • Autumn K, Liang YA, Hsieh ST, Zesch W, Chan WP, Kenny TW, Fearing R, Full RJ (2000) Adhesive force of a single gecko foot-hair. Nature 405: 681–685

    Article  CAS  Google Scholar 

  • Autumn K, Peattie AM (2002) Mechanisms of adhesion in geckos. Int Comp Biol 42: 1081–1090

    Article  Google Scholar 

  • Bergmann PJ, Irschick DJ (2005) Effects of temperature on maximum clinging ability in a diurnal gecko: evidence for a passive clinging mechanism?. J Exp Zool 303A: 785–791

    Article  Google Scholar 

  • Boettger J (1997) All-electron full-potential calculation of the electronic band structure, elastic constants, and equation of state for graphite. Phys Rev B 55(17): 11202–11211

    Article  CAS  Google Scholar 

  • Dellit WD (1934) Zur anatomie und physiologie der geckozehe. Z Naturwiss 68: 613–656

    Google Scholar 

  • Gao H, Wang X, Yao H, Gorb S, Arzt E (2005) Mechanics of hierarchical adhesion structures of geckos. Mech Mater 37: 275–285

    Article  Google Scholar 

  • Gennaro JGJ (1969) The gecko grip. Nat Hist 78: 36–43

    Google Scholar 

  • Girifalco LA, Hodak M, Lee RS (2000) Carbon nanotubes, buckyballs, ropes, and a universal graphitic potential. Phys Rev B 62(19):13104–13110. http://prb.aps.org/

    Google Scholar 

  • Girifalco LA, Lad RA (1956) Energy of cohesion, compressibility, and the potential energy functions of graphite system. J Chem Phys 25(4):693–697. http://jcp.aip.org/

    Google Scholar 

  • Gorb SN (2001) Attachment devices of insect cuticle. Kluwer Academic, Dordrecht

    Google Scholar 

  • Haeshin L, Bruce PL, Phillip BM (2007) A reversible wet/dry adhesive inspired by mussels and geckos. Nature 448: 338–341

    Article  Google Scholar 

  • Hanfland M, Beister H, Syassen K (1989) Graphite under pressure: equation of state and first-order Raman modes. Phys Rev B 39(17): 12598–12603

    Article  CAS  Google Scholar 

  • Hiller U (1968) Untersuchungen zum feinbau und zur funktion der haftborsten von reptilien. Z Morphol Tiere 62: 307–362

    Article  Google Scholar 

  • Huber G, Gorb SN, Spolenak R, Arzt E (2005a) Resolving the nanoscale adhesion of individual gecko spatulae by atomic force microscopy. Biol Lett 1: 2–4

    Article  Google Scholar 

  • Huber G, Mantz H, Spolenak R, Mecke K, Jacobs K, Gorb SN, Arzt E (2005b) Evidence for capillarity contributions to gecko adhesion from single spatula nanomechanical measurements. Proc Natl Acad Sci USA 102: 16293–16296

    Article  CAS  Google Scholar 

  • Kendall K (1975) Thin-film peeling-the elastic term. J Phys D Appl Phys 8:1449–1452. http://iopscience.iop.org/0022-3727

    Google Scholar 

  • Pugno NM (2007) Towards a spiderman suit: large invisible cables and self-cleaning releasable super-adhesive materials. J Phys: Condens Matter 19: 395001

    Article  Google Scholar 

  • Pugno NM (2008) Spiderman gloves. Nano Today 3: 36–42

    Article  Google Scholar 

  • Pugno N, Lepore E (2008) Observation of optimal gecko’s adhesion on nanorough surfaces. Biosystems 94: 218–222

    Article  Google Scholar 

  • Pugno N, Lepore E (2008) Living tokay geckos display adhesion times following the Weibull statistics. J Adhesion 84: 949–962

    Google Scholar 

  • Qian D, Liu WK, Ruoff RS (2001) Mechanics of C60 in nanotubes. J Phys Chem B 105: 10753–10758

    Article  CAS  Google Scholar 

  • Ruoff RS, Ruoff AL (1991) The bulk modulus of Ceo molecules and crystals: a molecular mechanical approach. Appl Phys Lett 59(13): 1553–1555

    Article  CAS  Google Scholar 

  • Russell AP (1975) A contribution to the functional analysis of the foot of the Tokay, Gekko gecko (Reptilia: Gekkonidae). J Zool Lond 176: 437–476

    Article  Google Scholar 

  • Russell AP (1986) The morphological basis of weight-bearing in the scansors of the tokay gecko (Repitilia: Sautia). Can J Zool 64: 948–955

    Article  Google Scholar 

  • Ruibal R, Ernst V (1965) The structure of the digital setae of lizards. J Morphol 117:271–294. http://onlinelbrary.wiley.com/journal/10.1002/(ISSN)1097-4687

    Google Scholar 

  • Schleich HH, Kästle W (1986) Ultrastrukturen an gecko-zehen (Reptilia: Sauria: Gekkonidae). Amphib Reptil 7: 141–166

    Article  Google Scholar 

  • Schmidt HR (1904) Zur anatomie und physiologie der geckopfote. Z Naturwiss 39: 551–563

    Google Scholar 

  • Simmermacher G (1884) Untersuchungen über haftapparate an tarsalgliedern von insekten . Zeitschr Wiss Zool 40: 481–556

    Google Scholar 

  • Spurr AR (1969) A low-viscosity epoxy resin embedding medium for electron microscopy. J Ultrastruct Res 26: 31–43

    Article  CAS  Google Scholar 

  • Stork NE (1980) Experimental analysis of adhesion of Chrysopolina polita (Chrysomelidae: Coleoptera) on a variety of surfaces. J Exp Biol 88: 91–107

    Google Scholar 

  • Yurdumakan B, Raravikar NR, Ajayanm PM, Dhinojwala A (2005) Synthetic gecko foot-hairs from multiwalled carbon nanotubes. Chem Commun 30: 3799–3801

    Article  Google Scholar 

  • Zhao YX, Spain IL (1989) X-ray diffraction data for graphite to 20 GPa. Phys Rev B 40(2):993–997. http://prb.aps.org/

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Nicola M. Pugno.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Pantano, A., Pugno, N.M. & Gorb, S.N. Numerical simulations demonstrate that the double tapering of the spatualae of lizards and insects maximize both detachment resistance and stability. Int J Fract 171, 169–175 (2011). https://doi.org/10.1007/s10704-011-9596-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-011-9596-8

Keywords

Navigation