Skip to main content
Log in

Auxetic mechanical metamaterials with diamond and elliptically shaped perforations

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

Mechanical metamaterials are systems which derive their mechanical properties from their structure rather than their intrinsic material composition. In this work, we investigate a class of highly anisotropic mechanical metamaterials designed by the introduction of diamond and elliptically shaped perforations which possess the ability to show auxetic behaviour. By the use of finite element simulations, we show how these highly tuneable systems have the potential to exhibit a large range of Poisson’s ratios, ranging from highly positive to giant negative values, simply by altering the geometric parameters and orientation of the perforations. The anomalous properties of these systems have also been shown to be retained over significant tensile strain ranges, highlighting the vast potential applicability and functionality of these mechanical metamaterials.

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.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8: a
Fig. 9

Similar content being viewed by others

References

  1. Evans, K.E., Nkansah, M.A., Hutchinson, I.J., Rogers, J.A.: Molecular network design. Nature 353, 124 (1991)

    Article  Google Scholar 

  2. Ali, M.N., Rehman, I.U.: Auxetic polyurethane stents and stent-grafts for the palliative treatment of squamous cell carcinomas of the proximal and mid oesophagus: a novel fabrication route. J. Manuf. Syst. (2014). https://doi.org/10.1016/j.jmsy.2014.07.009

    Article  Google Scholar 

  3. Mizzi, L., Attard, D., Casha, A., Grima, J.N., Gatt, R.: On the suitability of hexagonal honeycombs as stent geometries. Phys. Status Solidi B 251, 328–337 (2014). https://doi.org/10.1002/pssb.201384255

    Article  Google Scholar 

  4. Wu, W., Song, X., Liang, J., Xia, R., Qian, G., Fang, D.: Mechanical properties of anti-tetrachiral auxetic stents. Compos. Struct. 185, 381–392 (2018). https://doi.org/10.1016/j.compstruct.2017.11.048

    Article  Google Scholar 

  5. Grima, J.N., Evans, K.E.: Auxetic slit-perforated sheets with a “Rotating Squares” geometry and their applicability for the manufacture of knee and elbow bandages (Personal Communication) (2000)

  6. Wright, J.R., Burns, M.K., James, E., Sloan, M.R., Evans, K.E.: On the design and characterisation of low-stiffness auxetic yarns and fabrics. Text. Res. J. 82, 645–654 (2012)

    Article  Google Scholar 

  7. Wang, Z., Hong, H.: A finite element analysis of an auxetic wrap-knitted spacer fabric structure. Text. Res. J. 85, 404–415 (2014)

    Article  Google Scholar 

  8. Gatt, R., Mizzi, L., Azzopardi, J.I., Azzopardi, K.M., Attard, D., Casha, A., et al.: Hierarchical auxetic mechanical metamaterials. Sci. Rep. 5, 1–6 (2015). https://doi.org/10.1038/srep08395

    Article  Google Scholar 

  9. Mizzi, L., Azzopardi, K.M., Attard, D., Grima, J.N., Gatt, R.: Auxetic metamaterials exhibiting giant negative Poisson’s ratios. Phys. Status Solidi Rapid Res. Lett. 9, 425–430 (2015). https://doi.org/10.1002/pssr.201510178

    Article  Google Scholar 

  10. Abramovitch, H., Burgard, M., Edery-Azulay, L., Evans, K.E., Hoffmeister, M., Miller, W., et al.: Smart tetrachiral and hexachiral honeycomb: sensing and impact detection. Compos. Sci. Technol. 70, 1072–1079 (2010). https://doi.org/10.1016/j.compscitech.2009.07.017

    Article  Google Scholar 

  11. Jacobs, S., Coconnier, C., Dimaio, D., Scarpa, F., Toso, M., Martinez, J.: Deployable auxetic shape memory alloy cellular antenna demonstrator: design, manufacturing and modal testing. Smart Mater. Struct. (2012). https://doi.org/10.1088/0964-1726/21/7/075013

    Article  Google Scholar 

  12. Scarpa, F., Jacobs, S., Coconnier, C., Toso, M., Di Maio, D.: Auxetic shape memory alloy cellular structures for deployable satellite antennas: design, manufacture and testing. EPJ Web Conf. 6, 27001 (2010). https://doi.org/10.1051/epjconf/20100627001

    Article  Google Scholar 

  13. Airoldi, A., Bettini, P., Panichelli, P., Oktem, M.F., Sala, G.: Chiral topologies for composite morphing structures—Part I: development of a chiral rib for deformable airfoils. Phys. Status Solidi Basic Res. 252, 1435–1445 (2015). https://doi.org/10.1002/pssb.201451689

    Article  Google Scholar 

  14. Olympio, K.R., Gandhi, F.: Zero Poisson’s ratio cellular honeycombs for flex skins undergoing one-dimensional morphing. J. Intell. Mater. Syst. Struct. 21, 1737–1753 (2010)

    Article  Google Scholar 

  15. Spadoni, A., Ruzzene, M.: Static aeroelastic response of chiral-core airfoils. J. Intell. Mater. Syst. Struct. 18, 1067–1075 (2007). https://doi.org/10.1177/1045389X06072361

    Article  Google Scholar 

  16. Airoldi, A., Bettini, P., Panichelli, P., Sala, G.: Chiral topologies for composite morphing structures—Part II: novel configurations and technological processes. Phys. Status Solidi Basic Res. 252, 1446–1454 (2015). https://doi.org/10.1002/pssb.201584263

    Article  Google Scholar 

  17. Crumm, A.T., Halloran, Æ.J.W.: Negative Poisson’ s ratio structures produced from zirconia and nickel using co-extrusion 1336–1342 (2007). https://doi.org/10.1007/s10853-006-1209-y

  18. Schwerdtfeger, J., Heinl, P., Singer, R.F., Korner, C.: Auxetic cellular structures through selective electron-beam melting. Phys. Status Solidi 247, 269–272 (2010). https://doi.org/10.1002/pssb.200945513

    Article  Google Scholar 

  19. Hengsbach, S., Lantada, A.D.: Direct laser writing of auxetic structures: present capabilities and challenges. Smart Mater. Struct. 23, 085033 (2014)

    Article  Google Scholar 

  20. Ren, X., Shen, J., Ghaedizadeh, A., Tian, H., Xie, Y.M.: Experiments and parametric studies on 3D metallic auxetic metamaterials with tuneable mechanical properties. Smart Mater. Struct. 24, 095016 (2015). https://doi.org/10.1088/0964-1726/24/9/095016

    Article  Google Scholar 

  21. Bückmann, T., Stenger, N., Kadic, M., Kaschke, J., Frölich, A., Kennerknecht, T., et al.: Tailored 3D mechanical metamaterials made by dip-in direct-laser-writing optical lithography. Adv. Mater. (2012). https://doi.org/10.1002/adma.201200584

    Article  Google Scholar 

  22. Babaee, S., Shim, J., Weaver, J.C., Chen, E.R.: Patel N. 3D Soft Metamaterials with Negative Poisson’ s Ratio (2013). https://doi.org/10.1002/adma.201301986

  23. Mizzi, L., Mahdi, E.M., Titov, K., Gatt, R., Attard, D., Evans, K.E., et al.: Mechanical metamaterials with star-shaped pores exhibiting negative and zero Poisson’s ratio. Mater. Des. 146, 28–37 (2018). https://doi.org/10.1016/j.matdes.2018.02.051

    Article  Google Scholar 

  24. Hohmann, J.K., Renner, M., Waller, E.H., von Freymann, G.: Three-dimensional u-printing: an enabling technology. Adv. Opt. Mater. 3, 1488–1507 (2015)

    Article  Google Scholar 

  25. Meza, L.R., Zelhofer, A.J., Clarke, N., Mateos, A.J., Kochmann, D.M., Greer, J.R.: Resilient 3D hierarchical architected metamaterials. Proc. Natl. Acad. Sci. 112, 11502–11507 (2015). https://doi.org/10.1073/pnas.1509120112

    Article  Google Scholar 

  26. Zheng, X., Smith, W., Jackson, J., Moran, B., Cui, H., Chen, D., et al.: Multiscale metallic metamaterials. Nat. Mater. 15, 1100–1107 (2016). https://doi.org/10.1038/NMAT4694

    Article  Google Scholar 

  27. Clausen, A., Wang, F., Jensen, J.S., Sigmund, O., Lewis, J.A.: Topology optimized architectures with programmable Poisson’s ratio over large deformations. Adv. Mater. 27, 5523–5527 (2015). https://doi.org/10.1002/adma.201502485

    Article  Google Scholar 

  28. Ling, B., Wei, K., Wang, Z., Yang, X., Qu, Z., Fang, D.: Experimentally program large magnitude of Poisson’s ratio in additively manufactured mechanical metamaterials. Int. J. Mech. Sci. 173, 105466 (2020). https://doi.org/10.1016/j.ijmecsci.2020.105466

    Article  Google Scholar 

  29. Dudek, K.K., Attard, D., Gatt, R., Grima-Cornish, J.N., Grima, J.N.: The multidirectional auxeticity and negative linear compressibility of a 3D mechanical metamaterial. Mater. Basel 13, 1–16 (2020). https://doi.org/10.3390/ma13092193

    Article  Google Scholar 

  30. Grima, J.N., Gatt, R.: Perforated sheets exhibiting negative Poisson’s ratios. Adv. Eng. Mater. 12, 460–464 (2010). https://doi.org/10.1002/adem.201000005

    Article  Google Scholar 

  31. Grima, J.N., Gatt, R., Ellul, B., Chetcuti, E.: Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations. J. Non Cryst. Solids 356, 1980–1987 (2010). https://doi.org/10.1016/j.jnoncrysol.2010.05.074

    Article  Google Scholar 

  32. Bertoldi, B.K., Reis, P.M., Willshaw, S., Mullin, T.: Negative Poisson’ s ratio behavior induced by an elastic instability. Adv. Funct. Mater. (2009). https://doi.org/10.1002/adma.200901956

    Article  Google Scholar 

  33. Shim, J., Shan, S., Košmrlj, A., Kang, S.H., Chen, E.R., Weaver, J.C., et al.: Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials. Soft Matter 9, 8198–8202 (2013). https://doi.org/10.1039/c3sm51148k

    Article  Google Scholar 

  34. Shen, J., Zhou, S., Huang, X., Xie, Y.M.: Simple cubic three-dimensional auxetic metamaterials. Phys. Status Solidi B Basic Res. 8, 1–8 (2014). https://doi.org/10.1002/pssb.201451304

    Article  Google Scholar 

  35. Slann, A., White, W., Scarpa, F., Boba, K., Farrow, I.: Cellular plates with auxetic rectangular perforations. Phys. Status Solidi 252, 1533–1539 (2015). https://doi.org/10.1002/pssb.201451740

    Article  Google Scholar 

  36. Cho, Y., Shin, J., Costa, A., Ann, T., Kunin, V., Li, J., et al.: Engineering the shape and structure of materials by fractal cut. Proc. Natl. Acad. Sci. 111, 17390–17395 (2014). https://doi.org/10.1073/pnas.1417276111

    Article  Google Scholar 

  37. Tang, Y., Lin, G., Han, L., Qiu, S., Yang, S., Yin, J.: Design of hierarchically cut hinges for highly stretchable and reconfigurable metamaterials with enhanced strength. Adv. Mater. (2015). https://doi.org/10.1002/adma.201502559

    Article  Google Scholar 

  38. Tang, Y., Yin, J.: Design of cut unit geometry in hierarchical kirigami-based auxetic metamaterials for high stretchability and compressibility. Extrem. Mech. Lett. 12, 77–85 (2017). https://doi.org/10.1016/j.eml.2016.07.005

    Article  Google Scholar 

  39. Shan, S., Kang, S.H., Zhao, Z., Fang, L., Bertoldi, K.: Design of planar isotropic negative Poisson’s ratio structures. Extrem. Mech. Lett. 4, 96–102 (2015). https://doi.org/10.1016/j.eml.2015.05.002

    Article  Google Scholar 

  40. Taylor, M., Francesconi, L., Gerendás, M., Shanian, A., Carson, C., Bertoldi, K.: Low porosity metallic periodic structures with negative Poisson’s ratio. Adv. Mater. 26, 2365–2370 (2014)

    Article  Google Scholar 

  41. Mizzi, L., Grima, J.N., Gatt, R., Attard, D.: Analysis of the deformation behavior and mechanical properties of slit-perforated auxetic metamaterials. Phys. Status Solidi (2019). https://doi.org/10.1002/pssb.201800153

    Article  Google Scholar 

  42. Wu, G., Cho, Y., Choi, I., Ge, D., Li, J., Han, H.N., et al.: Directing the deformation paths of soft metamaterials with prescribed asymmetric units. Adv. Mater. (2015). https://doi.org/10.1002/adma.201500716

    Article  Google Scholar 

  43. Mizzi, L., Salvati, E., Spaggiari, A., Tan, J., Korsunsky, A.M.: Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting. Int. J. Mech. Sci. 167, 105242 (2020). https://doi.org/10.1016/j.ijmecsci.2019.105242

    Article  Google Scholar 

  44. Wang, G., Sun, S., Li, M., Zhou, J.: Large deformation shape optimization of cut-mediated soft mechanical metamaterials. Mater. Res. Express 6, 055802 (2019)

    Article  Google Scholar 

  45. Grima, J.N., Mizzi, L., Azzopardi, K.M., Gatt, R.: Auxetic perforated mechanical metamaterials with randomly oriented cuts. Adv. Mater. 28, 385–389 (2016). https://doi.org/10.1002/adma.201503653

    Article  Google Scholar 

  46. Overvelde, J.T.B., Bertoldi, K.: Relating pore shape to the non-linear response of periodic elastomeric structures. J. Mech. Phys. Solids 64, 351–366 (2014). https://doi.org/10.1016/j.jmps.2013.11.014

    Article  Google Scholar 

  47. Rafsanjani, A., Pasini, D.: Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs. Extrem. Mech. Lett. 9, 291–296 (2016)

    Article  Google Scholar 

  48. Jin, L., Khajehtourian, R., Mueller, J., Rafsanjani, A., Tournat, V., Bertoldi, K., et al.: Guided transition waves in multistable mechanical metamaterials. Proc. Natl. Acad. Sci. 117, 2319–2325 (2020)

    Article  MathSciNet  Google Scholar 

  49. Grima, J.N., Evans, K.E.: Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 19, 1563–1565 (2000)

    Article  Google Scholar 

  50. Grima, J.N., Evans, K.E.: Auxetic behaviour from rotating triangles. J. Mater. Sci. 41, 3193–3196 (2006)

    Article  Google Scholar 

  51. Attard, D., Grima, J.N.: A three-dimensional rotating rigid units network exhibiting negative Poisson’s ratios. Phys. Status Solidi 249, 1330–1338 (2012)

    Article  Google Scholar 

  52. Grima, J.N., Alderson, A., Evans, K.E.: Negative Poisson’s ratios from rotating rectangles. Comput. Methods Sci. Technol. 10, 137–145 (2004)

    Article  Google Scholar 

  53. Grima, J.N., Alderson, A., Evans, K.E.: Auxetic behaviour from rotating rigid units. Phys. Status Solidi 575, 561–575 (2005). https://doi.org/10.1002/pssb.200460376

    Article  Google Scholar 

  54. Grima, J.N., Gatt, R., Alderson, A., Evans, K.E.: On the auxetic properties of ‘rotating rectangles’ with different connectivity. J. Phys. Soc. Jpn. 74, 2866–2867 (2005)

    Article  Google Scholar 

  55. Grima, J.N., Farrugia, P.-S., Gatt, R., Attard, D.: On the auxetic properties of rotating rhombi and parallelograms: a preliminary investigation. Phys. Status Solidi 245, 521–529 (2008)

    Article  Google Scholar 

  56. Attard, D., Grima, J.N.: Auxetic behaviour from rotating rhombi. Phys. Status Solidi 245, 2395–2404 (2008). https://doi.org/10.1002/pssb.200880269

    Article  Google Scholar 

  57. Attard, D., Manicaro, E., Grima, J.N.: On rotating rigid parallelograms and their potential for exhibiting auxetic behaviour. Phys. Status Solidi B 2044, 2033–2044 (2009). https://doi.org/10.1002/pssb.200982034

    Article  Google Scholar 

  58. Taylor, M., Francesconi, L., Gerendás, M., Shanian, A., Carson, C.: Low porosity metallic periodic structures with negative Poisson’ s ratio. Adv. Mater. (2013). https://doi.org/10.1002/adma.201304464

    Article  Google Scholar 

  59. ANSYS® Academic Research Mechanical, Release 13.0 n.d

  60. Mizzi, L., Attard, D., Gatt, R., Dudek, K.K., Ellul, B., Grima, J.N.: Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis. Eng. Comput. (2020). https://doi.org/10.1007/s00366-019-00910-1

    Article  Google Scholar 

  61. Smith, C.W., Wooton, R.J., Evans, K.E.: Interpretation of experimental data for Poisson’s ratio of highly nonlinear materials. Exp. Mech. 39, 356–362 (1999)

    Article  Google Scholar 

  62. Grima, J.N., Winczewski, S., Mizzi, L., Grech, M.C., Cauchi, R., Gatt, R., et al.: Tailoring graphene to achieve negative Poisson’s ratio properties. Adv. Mater. 27, 1455–1459 (2015). https://doi.org/10.1002/adma.201404106

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to Ruben Gatt or Joseph N. Grima.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mizzi, L., Attard, D., Evans, K.E. et al. Auxetic mechanical metamaterials with diamond and elliptically shaped perforations. Acta Mech 232, 779–791 (2021). https://doi.org/10.1007/s00707-020-02881-7

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-020-02881-7

Navigation