Skip to main content

Durable bistable auxetics made of rigid solids

  • Xiao Shang (a1), Lu Liu (a1), Ahmad Rafsanjani (a2) and Damiano Pasini (a1)

Bistable Auxetic Metamaterials (BAMs) are a class of monolithic perforated periodic structures with negative Poisson’s ratio. Under tension, a BAM can expand and reach a second state of equilibrium through a globally large shape transformation that is ensured by the flexibility of its elastomeric base material. However, if made from a rigid polymer, or metal, BAM ceases to function due to the inevitable rupture of its ligaments. The goal of this work is to extend the unique functionality of the original kirigami architecture of BAM to a rigid solid base material. We use experiments and numerical simulations to assess performance, bistability, and durability of rigid BAMs at 10,000 cycles. Geometric maps are presented to elucidate the role of the main descriptors of the BAM architecture. The proposed design enables the realization of BAM from a large palette of materials, including elastic-perfectly plastic materials and potentially brittle materials.

  • View HTML
    • Send article to Kindle

      To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      Durable bistable auxetics made of rigid solids
      Available formats
      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      Durable bistable auxetics made of rigid solids
      Available formats
      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      Durable bistable auxetics made of rigid solids
      Available formats
Corresponding author
a) Address all correspondence to this author. e-mail:
Hide All

Contributing Editor: Katia Bertoldi

Hide All
1. Pendry, J.B., Holden, A.J., Robbins, D.J., and Stewart, W.J.: Magnetism from conductors and enhanced nonlinear phenomena. IEEE Trans. Microwave Theory Tech. 47, 2075 (1999).
2. Lee, J.H., Singer, J.P., and Thomas, E.L.: Micro-/nanostructured mechanical metamaterials. Adv. Mater. 24, 4782 (2012).
3. Ding, Y., Liu, Z., Qiu, C., and Shi, J.: Metamaterial with simultaneously negative bulk modulus and mass density. Phys. Rev. Lett. 99, 093904 (2007).
4. Liu, X., Hu, G., Huang, G., and Sun, C.: An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl. Phys. Lett. 98, 251907 (2011).
5. Kadic, M., Bückmann, T., Stenger, N., Thiel, M., and Wegener, M.: On the practicability of pentamode mechanical metamaterials. Appl. Phys. Lett. 100, 191901 (2012).
6. Milton, G.W.: Composite materials with poisson’s ratios close to—1. J. Mech. Phys. Solids 40, 1105 (1992).
7. Rafsanjani, A., Akbarzadeh, A., and Pasini, D.: Snapping mechanical metamaterials under tension. Adv. Mater. 27, 5931 (2015).
8. Haghpanah, B., Salari-Sharif, L., Pourrajab, P., Hopkins, J., and Valdevit, L.: Multistable shape-reconfigurable architected materials. Adv. Mater. 28, 7915 (2016).
9. Greaves, G.N., Greer, A.L., Lakes, R.S., and Rouxel, T.: Poisson’s ratio and modern materials. Nat. Mater. 10, 823 (2011).
10. Evans, K.E., Nkansah, M.A., Hutchinson, I.J., and Rogers, S.C.: Molecular network design. Nature 353, 124 (1991).
11. Lakes, R.: Foam structures with a negative Poisson’s ratio. Science 235, 1038 (1987).
12. Ali, M.N., Busfield, J.J.C., and Rehman, I.U.: Auxetic oesophageal stents: Structure and mechanical properties. J. Mater. Sci.: Mater. Med. 25, 527 (2014).
13. Gatt, R., Mizzi, L., Azzopardi, J.I., Azzopardi, K.M., Attard, D., Casha, A., Briffa, J., and Grima, J.N.: Hierarchical auxetic mechanical metamaterials. Sci. Rep. 5, 8395 (2015).
14. Scarpa, F., Ciffo, L.G., and Yates, J.R.: Dynamic properties of high structural integrity auxetic open cell foam. Smart Mater. Struct. 13, 49 (2004).
15. Taylor, M., Francesconi, L., Gerendás, M., Shanian, A., Carson, C., and Bertoldi, K.: Low porosity metallic periodic structures with negative Poisson’s ratio. Adv. Mater. 26, 2365 (2014).
16. Javid, F., Liu, J., Rafsanjani, A., Schaenzer, M., Pham, M.Q., Backman, D., Yandt, S., Innes, M.C., Booth-Morrison, C., Gerendas, M., Scarinci, T., Shanian, A., and Bertoldi, K.: On the design of porous structures with enhanced fatigue life. Extreme Mech. Lett. 16, 13 (2017).
17. Grima, J.N. and Gatt, R.: Perforated sheets exhibiting negative Poisson’s ratios. Adv. Eng. Mater. 12, 460 (2010).
18. Grima, J.N., Mizzi, L., Azzopardi, K.M., and Gatt, R.: Auxetic perforated mechanical metamaterials with randomly oriented cuts. Adv. Mater. 28, 385 (2016).
19. Yasuda, H. and Yang, J.: Reentrant origami-based metamaterials with negative Poisson’s ratio and bistability. Phys. Rev. Lett. 114, 185502 (2015).
20. Filipov, E.T., Tachi, T., and Paulino, G.H.: Origami tubes assembled into stiff, yet reconfigurable structures and metamaterials. Proc. Natl. Acad. Sci. U. S. A. 112, 12321 (2015).
21. Bertoldi, K., Reis, P.M., Willshaw, S., and Mullin, T.: Negative Poisson’s ratio behavior induced by an elastic instability. Adv. Mater. 22, 361 (2010).
22. Ghaedizadeh, A., Shen, J., Ren, X., and Xie, Y.M.: Tuning the performance of metallic auxetic metamaterials by using buckling and plasticity. Materials 9, 54 (2016).
23. Findeisen, C., Hohe, J., Kadic, M., and Gumbsch, P.: Characteristics of mechanical metamaterials based on buckling elements. J. Mech. Phys. Solids 102, 151 (2017).
24. Babaee, S., Shim, J., Weaver, J.C., Chen, E.R., Patel, N., and Bertoldi, K.: 3D soft metamaterials with negative Poisson’s ratio. Adv. Mater. 25, 5044 (2013).
25. Prasad, J. and Diaz, A.R.: Synthesis of bistable periodic structures using topology optimization and a genetic algorithm. J. Mech. Des. 128, 1298 (2005).
26. Restrepo, D., Mankame, N.D., and Zavattieri, P.D.: Phase transforming cellular materials. Extreme Mech. Lett. 4, 52 (2015).
27. Hewage, T.A.M., Alderson, K.L., Alderson, A., and Scarpa, F.: Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative Poisson’s ratio properties. Adv. Mater. 28, 10323 (2016).
28. Silverberg, J.L., Na, J-H., Evans, A.A., Liu, B., Hull, T.C., Santangelo, C.D., Lang, R.J., Hayward, R.C., and Cohen, I.: Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater. 14, 389 (2015).
29. Rafsanjani, A. and Pasini, D.: Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs. Extreme Mech. Lett. 9(Part 2), 291 (2016).
30. Jensen, B.D., Howell, L.L., and Salmon, L.G.: Design of two-link, in-plane, bistable compliant micro-mechanisms. J. Mech. Des 121, 416 (1999).
31. Hanaor, A. and Levy, R.: Evaluation of deployable structures for space enclosures. Int. J. Space Struct. 16, 211 (2001).
32. Zhao, J-S., Chu, F., and Feng, Z-J.: The mechanism theory and application of deployable structures based on SLE. Mech. Mach. Theory 44, 324 (2009).
33. Masoumi Khalil Abad, E., Arabnejad Khanoki, S., and Pasini, D.: Fatigue design of lattice materials via computational mechanics: Application to lattices with smooth transitions in cell geometry. Int. J. Fatigue 47, 126 (2013).
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Materials Research
  • ISSN: 0884-2914
  • EISSN: 2044-5326
  • URL: /core/journals/journal-of-materials-research
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Type Description Title
Supplementary materials

Shang et al supplementary material
Shang et al supplementary material 1

 Video (27.2 MB)
27.2 MB


Altmetric attention score

Full text views

Total number of HTML views: 34
Total number of PDF views: 193 *
Loading metrics...

Abstract views

Total abstract views: 815 *
Loading metrics...

* Views captured on Cambridge Core between 6th November 2017 - 22nd March 2018. This data will be updated every 24 hours.