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Nonlinear material behaviour of spider silk yields robust webs

Nature volume 482, pages 72–76 (2012)Cite this article

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Abstract

Natural materials are renowned for exquisite designs that optimize function, as illustrated by the elasticity of blood vessels, the toughness of bone and the protection offered by nacre1,2,3,4,5. Particularly intriguing are spider silks, with studies having explored properties ranging from their protein sequence6 to the geometry of a web7. This material system8, highly adapted to meet a spider’s many needs, has superior mechanical properties9,10,11,12,13,14,15. In spite of much research into the molecular design underpinning the outstanding performance of silk fibres1,6,10,13,16,17, and into the mechanical characteristics of web-like structures18,19,20,21, it remains unknown how the mechanical characteristics of spider silk contribute to the integrity and performance of a spider web. Here we report web deformation experiments and simulations that identify the nonlinear response of silk threads to stress—involving softening at a yield point and substantial stiffening at large strain until failure—as being crucial to localize load-induced deformation and resulting in mechanically robust spider webs. Control simulations confirmed that a nonlinear stress response results in superior resistance to structural defects in the web compared to linear elastic or elastic–plastic (softening) material behaviour. We also show that under distributed loads, such as those exerted by wind, the stiff behaviour of silk under small deformation, before the yield point, is essential in maintaining the web’s structural integrity. The superior performance of silk in webs is therefore not due merely to its exceptional ultimate strength and strain, but arises from the nonlinear response of silk threads to strain and their geometrical arrangement in a web.

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Figure 1: Material behaviour of dragline spider silk, web model, and behaviour of webs under load.
Figure 2: Web response for varied silk behaviour under targeted (local) and distributed (global) loading.
Figure 3: Effects of stress–strain behaviour on structural robustness via quantized fracture mechanics.

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Acknowledgements

This work was supported primarily by the Office of Naval Research (N000141010562) with additional support from the National Science Foundation (MRSEC DMR-0819762, the NSF-REU programme, as well as CMMI-0642545) and the Army Research Office (W911NF-09-1-0541 and W911NF-10-1-0127). Support from the MIT-Italy programme (MITOR) and a Robert A. Brown Presidential Fellowship is gratefully acknowledged. N.M.P. is supported by the METREGEN grant (2009-2012) “Metrology on a cellular and macromolecular scale for regenerative medicine”. An Ideas Starting Grant 2011 BIHSNAM on “Bio-inspired hierarchical super nanomaterials” was awarded to N.M.P. from the European Research Council, under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant (agreement number 279985). All simulations have been carried out at MIT’s Laboratory for Atomistic and Molecular Mechanics (LAMM). We acknowledge assistance from S. and E. Buehler in taking photographs of the spider web.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Laboratory for Atomistic and Molecular Mechanics (LAMM), Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA,

    Steven W. Cranford, Anna Tarakanova & Markus J. Buehler

  2. Center for Materials Science and Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA ,

    Steven W. Cranford, Anna Tarakanova & Markus J. Buehler

  3. Department of Applied and Engineering Physics, Cornell University, Ithaca, 14853, New York, USA

    Anna Tarakanova

  4. Department of Structural Engineering and Geotechnics, Laboratory of Bio-Inspired Nanomechanics “Giuseppe Maria Pugno”, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy,

    Nicola M. Pugno

  5. Center for Computational Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, USA ,

    Markus J. Buehler

Authors
  1. Steven W. Cranford
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  2. Anna Tarakanova
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  4. Markus J. Buehler
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Contributions

S.W.C. and M.J.B. designed the research and analysed the results. S.W.C. and A.T. developed the material models, performed the simulations, and conducted the simulation data analysis. M.J.B. performed the in situ experiments and analysed the results. N.M.P. contributed the theoretical analysis and predictions and analysed the results. S.W.C., M.J.B., A.T. and N.M.P. wrote the paper.

Corresponding author

Correspondence to Markus J. Buehler.

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The authors declare no competing financial interests.

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This file contains Supplementary Text and Data 1-11, Supplementary Figures 1-12 with legends, Supplementary Tables 1-5 and additional references. (PDF 1128 kb)

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Cranford, S., Tarakanova, A., Pugno, N. et al. Nonlinear material behaviour of spider silk yields robust webs. Nature 482, 72–76 (2012). https://doi.org/10.1038/nature10739

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