Bioinspired kirigami metasurfaces as assistive shoe grips


Falls and subsequent complications are major contributors to morbidity and mortality, especially in older adults. Here, by taking inspiration from claws and scales found in nature, we show that buckling kirigami structures applied to footwear outsoles generate higher friction forces in the forefoot and transversally to the direction of movement. We identified optimal kirigami designs capable of modulating friction for a range of surfaces, including ice, by evaluating the performance of the dynamic kirigami outsoles through numerical simulations and in vitro friction testing, as well as via human-gait force-plate measurements. We anticipate that lightweight kirigami metasurfaces applied to footwear outsoles could help mitigate the risk of slips and falls in a range of environments.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: Kirigami shoe grip for the dynamic modulation of friction and prevention of slips and falls.
Fig. 2: Mechanical characterization of the kirigami shoe grips with different spike shapes.
Fig. 3: Friction enhancement of the kirigami shoe grips with various spike shapes and arrangements.
Fig. 4: Kirigami shoe grip-induced changes in utilized friction coefficient on an ice surface.

Data availability

The main data supporting the results of this study are available within the paper and its Supplementary Information. All of the data generated in this study, including the source data and the data used to make the figures, are available from figshare with the identifier

Code availability

The ABAQUS scripts used for the numerical analyses are available as Supplementary Information.


  1. 1.

    Injury Facts. National Safety Council (2017).

  2. 2.

    Li, K., Courtney, T. & Huang, Y. Slipping and falling experience and perception of floor slipperiness: a field survey in 10 fast-food restaurants in Taiwan. Prof. Saf. 51, 34–38 (2006).

    Google Scholar 

  3. 3.

    Morrison, R., Chassin, M. & Siu, A. The medical consultant’s role in caring for patients with hip fracture. Ann. Intern. Med. 128, 1010–1020 (1998).

    CAS  PubMed  Google Scholar 

  4. 4.

    Wolinsky, F. D., Fitzgerald, J. F. & Stump, T. E. The effect of HIP fracture on mortality, hospitalization, and functional status: a prospective study. Am. J. Public Health 87, 398–403 (1997).

    CAS  PubMed  PubMed Central  Google Scholar 

  5. 5.

    Panula, J. et al. Mortality and cause of death in hip fracture patients aged 65 or older—a population-based study. BMC Musculoskelet. Disord. 12, 105 (2011).

    PubMed  PubMed Central  Google Scholar 

  6. 6.

    LeBlanc, E. S. et al. Hip fracture and increased short-term but not long-term mortality in healthy older women. Arch. Intern. Med. 171, 1831–1837 (2011).

    PubMed  PubMed Central  Google Scholar 

  7. 7.

    Tinetti, M. E. et al. A multifactorial intervention to reduce the risk of falling among elderly people living in the community. N. Engl. J. Med. 331, 821–827 (1994).

    CAS  PubMed  Google Scholar 

  8. 8.

    Englander, F., Hodson, T. & Terregrossa, R. Economic dimensions of slip and fall injuries. J. Forensic Sci. 41, 733–746 (1996).

    CAS  PubMed  Google Scholar 

  9. 9.

    Hsu, J. et al. Slip resistance of winter footwear on snow and ice measured using maximum achievable incline. Ergonomics 59, 717–728 (2016).

    PubMed  Google Scholar 

  10. 10.

    Stevens, J. A., Corso, P. S., Finkelstein, E. A. & Miller, T. R. The costs of fatal and non-fatal falls among older adults. Inj. Prev. 12, 290–295 (2006).

    CAS  PubMed  PubMed Central  Google Scholar 

  11. 11.

    Bureau of Labor Statistics, US Department of Labor. 42,480 work injuries involved ice, sleet, or snow in 2014. The Economics Daily (2016).

  12. 12.

    Chang, W. R., Leclercq, S., Lockhart, T. E. & Haslam, R. State of science: occupational slips, trips and falls on the same level. Ergonomics 59, 861–883 (2016).

    PubMed  PubMed Central  Google Scholar 

  13. 13.

    Hanson, J. P., Redfern, M. S. & Mazumdar, M. Predicting slips and falls considering required and available friction. Ergonomics 42, 1619–1633 (1999).

    CAS  PubMed  Google Scholar 

  14. 14.

    Gao, C. & Abeysekera, J. A systems perspective of slip and fall accidents on icy and snowy surfaces. Ergonomics 47, 573–598 (2004).

    PubMed  Google Scholar 

  15. 15.

    Gao, C., Holmér, I. & Abeysekera, J. Slips and falls in a cold climate: underfoot surface, footwear design and worker preferences for preventive measures. Appl. Ergon. 39, 385–391 (2008).

    PubMed  Google Scholar 

  16. 16.

    Bruce, M., Jones, C. & Manning, D. P. Slip-resistance on icy surfaces of shoes, crampons and chains—a new machine. J. Occup. Accid. 7, 273–283 (1986).

    Google Scholar 

  17. 17.

    Gard, G. & Berggård, G. Assessment of anti-slip devices from healthy individuals in different ages walking on slippery surfaces. Appl. Ergon. 37, 177–186 (2006).

    PubMed  Google Scholar 

  18. 18.

    Berggård, G. & Johansson, C. Pedestrians in wintertime—effects of using anti-slip devices. Accid. Anal. Prev. 42, 1199–1204 (2010).

    PubMed  Google Scholar 

  19. 19.

    Gao, C., Abeysekera, J., Hirvonen, M. & Grönqvist, R. Slip resistant properties of footwear on ice. Ergonomics 47, 710–716 (2004).

    PubMed  Google Scholar 

  20. 20.

    Menant, J. C., Steele, J. R., Menz, H. B., Munro, B. J. & Lord, S. R. Optimizing footwear for older people at risk of falls. J. Rehabil. Res. Dev. 45, 1167–1181 (2008).

    PubMed  Google Scholar 

  21. 21.

    Blees, M. K. et al. Graphene kirigami. Nature 524, 204–207 (2015).

    CAS  PubMed  Google Scholar 

  22. 22.

    Rafsanjani, A. & Bertoldi, K. Buckling-induced kirigami. Phys. Rev. Lett. 118, 084301 (2017).

    PubMed  Google Scholar 

  23. 23.

    Tang, Y. et al. Programmable kiri-kirigami metamaterials. Adv. Mater. 29, 1604262 (2017).

    Google Scholar 

  24. 24.

    Zhang, Y. et al. A mechanically driven form of kirigami as a route to 3D mesostructures in micro/nanomembranes. Proc. Natl Acad. Sci. USA 112, 11757–11764 (2015).

    CAS  PubMed  Google Scholar 

  25. 25.

    Liu, Z. et al. Nano-kirigami with giant optical chirality. Sci. Adv. 4, eaat4436 (2018).

    PubMed  PubMed Central  Google Scholar 

  26. 26.

    Wu, C., Wang, X., Lin, L., Guo, H. & Wang, Z. L. Paper-based triboelectric nanogenerators made of stretchable interlocking kirigami patterns. ACS Nano 10, 4652–4659 (2016).

    CAS  PubMed  Google Scholar 

  27. 27.

    Jang, N. S. et al. Simple approach to high-performance stretchable heaters based on kirigami patterning of conductive paper for wearable thermotherapy applications. ACS Appl. Mater. Interfaces 9, 19612–19621 (2017).

    CAS  PubMed  Google Scholar 

  28. 28.

    Rafsanjani, A., Zhang, Y., Liu, B., Rubinstein, S. M. & Bertoldi, K. Kirigami skins make a simple soft actuator crawl. Sci. Robot. 3, eaar7555 (2018).

    PubMed  Google Scholar 

  29. 29.

    Dias, M. A. et al. Kirigami actuators. Soft Matter 13, 9087–9092 (2017).

    CAS  PubMed  Google Scholar 

  30. 30.

    Zheng, W. et al. Kirigami-inspired highly stretchable nanoscale devices using multidimensional deformation of monolayer MoS 2. Chem. Mater. 30, 6063–6070 (2018).

    CAS  Google Scholar 

  31. 31.

    Morikawa, Y. et al. Ultrastretchable kirigami bioprobes. Adv. Healthc. Mater. 7, 1701100 (2018).

    Google Scholar 

  32. 32.

    Shyu, T. C. et al. A kirigami approach to engineering elasticity in nanocomposites through patterned defects. Nat. Mater. 14, 785–789 (2015).

    CAS  PubMed  Google Scholar 

  33. 33.

    Ma, R., Wu, C., Wang, Z. L. & Tsukruk, V. V. Pop-up conducting large-area biographene kirigami. ACS Nano 12, 9714–9720 (2018).

    CAS  PubMed  Google Scholar 

  34. 34.

    Song, Z. et al. Kirigami-based stretchable lithium-ion batteries. Sci. Rep. 5, 10988 (2015).

    CAS  PubMed  PubMed Central  Google Scholar 

  35. 35.

    Wilson, A. M. et al. Locomotion dynamics of hunting in wild cheetahs. Nature 498, 185–189 (2013).

    CAS  PubMed  Google Scholar 

  36. 36.

    Skutch, A. F. Helpers At Birds’ Nests: Cooperative Breeding and Related Behaviour (Univ. of Iowa Press, 1999).

  37. 37.

    Marvi, H. & Hu, D. L. Friction enhancement in concertina locomotion of snakes. J. R. Soc. Interface 9, 3067–3080 (2012).

    PubMed  PubMed Central  Google Scholar 

  38. 38.

    Guo, Z. V. & Mahadevan, L. Limbless undulatory propulsion on land. Proc. Natl Acad. Sci. USA 105, 3179–3184 (2008).

    CAS  PubMed  Google Scholar 

  39. 39.

    Suh, N. P. & Sin, H.-C. The genesis of friction. Wear 69, 91–114 (1981).

    CAS  Google Scholar 

  40. 40.

    Lee, D. W., Banquy, X. & Israelachvili, J. N. Stick-slip friction and wear of articular joints. Proc. Natl Acad. Sci. USA 110, 567–574 (2013).

    Google Scholar 

  41. 41.

    Das, S. et al. Stick–slip friction of gecko-mimetic flaps on smooth and rough surfaces. J. R. Soc. Interface 12, 20141346 (2015).

    PubMed  PubMed Central  Google Scholar 

  42. 42.

    Giakas, G. & Baltzopoulos, V. Time and frequency domain analysis of ground reaction forces during walking: an investigation of variability and symmetry. Gait Posture 5, 189–197 (1997).

    Google Scholar 

  43. 43.

    Lieberman, D. E. et al. Foot strike patterns and collision forces in habitually barefoot versus shod runners. Nature 463, 531–535 (2010).

    CAS  PubMed  Google Scholar 

  44. 44.

    Li, K. W. et al. The effect of shoe sole tread groove depth on the friction coefficient with different tread groove widths, floors and contaminants. Appl. Ergon. 37, 743–748 (2006).

    PubMed  Google Scholar 

  45. 45.

    Yamaguchi, T. & Hokkirigawa, K. Development of a high slip-resistant footwear outsole using a hybrid rubber surface pattern. Ind. Health 52, 414–423 (2014).

    PubMed  PubMed Central  Google Scholar 

  46. 46.

    Yamaguchi, T. et al. Efficacy of a rubber outsole with a hybrid surface pattern for preventing slips on icy surfaces. Appl. Ergon. 51, 9–17 (2015).

    PubMed  Google Scholar 

  47. 47.

    Rizvi, R., Naguib, H., Fernie, G. & Dutta, T. High friction on ice provided by elastomeric fiber composites with textured surfaces. Appl. Phys. Lett. 106, 111601 (2015).

    Google Scholar 

  48. 48.

    Ion, A., Kovacs, R., Schneider, O., Lopez, P., & Baudisch, P. Metamaterial textures. In Proc. CHI Conference on Human Factors in Computing Systems 336 (Association for Computing Machinery, 2018).

  49. 49.

    Iraqi, A., Cham, R., Redfern, M. S., Vidic, N. S. & Beschorner, K. E. Kinematics and kinetics of the shoe during human slips. J. Biomech. 74, 57–63 (2018).

    PubMed  PubMed Central  Google Scholar 

  50. 50.

    McGorry, R. W., Chang, C. C. & DiDomenico, A. Rearward movement of the heel at heel strike. Appl. Ergon. 39, 678–684 (2008).

    PubMed  Google Scholar 

  51. 51.

    Powers, C. M., Blanchette, M. G., Brault, J. R., Flynn, J. & Siegmund, G. P. Validation of walkway tribometers: establishing a reference standard. J. Forensic Sci. 55, 366–370 (2010).

    PubMed  Google Scholar 

  52. 52.

    Hsu, J., Li, Y., Dutta, T. & Fernie, G. Assessing the performance of winter footwear using a new maximum achievable incline method. Appl. Ergon. 50, 218–225 (2015).

    PubMed  Google Scholar 

Download references


We thank T. Hua, M. Cruz, N. Inverardi, X. Lu and V. Soares for their help with the experimental studies; S. Cotreau, C. Haynes and A. Wentworth for help with manufacturing the experimental specimens; and R. Langer for fruitful discussions. This work was funded in part by a start-up grant from the Deparment of Mechanical Engineering, MIT to G.T. K.B. acknowledges support from the National Science Foundation under grant nos. DMR-1420570 (Materials Research Science and Engineering Center) and EFRI C3 SoRo 1830896. A.R. acknowledges support from Swiss National Science Foundation grant no. P300P2-164648.

Author information




S.B., S.P., A.R., K.B. and G.T. conceived and designed the research. S.B., S.P. and A.R. designed the kirigami prototypes. S.B., S.P. and Y.S. performed the manufacturing, in vitro friction testing and human-gait force-plate measurements. A.R. performed the simulations. S.B., S.P., A.R., K.B. and G.T. discussed and analysed the results and wrote the manuscript. All authors reviewed the manuscript and provided active and valuable feedback.

Corresponding authors

Correspondence to Katia Bertoldi or Giovanni Traverso.

Ethics declarations

Competing interests

A.R. and K.B. are inventors on a patent application (patent no. US2019/0232598A1) describing buckling-induced kirigami. S.B., S.P., A.R., K.B. and G.T. are co-inventors on a provisional patent application (no. 62913419) for the technology described. Complete details of all relationships for profit and not for profit for G.T. can be found at the following link: The remaining authors disclose no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary notes, figures and video captions

Reporting Summary

Supplementary Video 1

Steel kirigami shoe grips attached to a shoe sole.

Supplementary Video 2

Finite-element simulation of a kirigami unit cell.

Supplementary Code 1

Linear post-buckling analysis for the kirigami simulator.

Supplementary Code 2

ABAQUS script for simulating buckling-induced kirigami.

Supplementary Code 3

Nonlinear post-buckling analysis and compression for the kirigami simulator.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Babaee, S., Pajovic, S., Rafsanjani, A. et al. Bioinspired kirigami metasurfaces as assistive shoe grips. Nat Biomed Eng 4, 778–786 (2020).

Download citation

Further reading


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing