Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs

Extreme Mechanics Letters

Volumn 9, Issue , 2016, Pages 291-296

  Rafsanjani, Ahmad ^a,b   Pasini, Damiano ^b  

^a HARVARD UNIVERSITY   (United States)

^b MCGILL UNIVERSITY   (Canada)

Author keywords

Auxetics; Mechanical metamaterials; Snap through Instability

Indexed keywords

BEAMS AND GIRDERS; FINITE ELEMENT METHOD; MECHANICAL TESTING;

AUXETIC MATERIALS; AUXETICS; DESIGN PRINCIPLES; FINITE ELEMENT SIMULATIONS; MATERIAL CONCEPTS; NEGATIVE POISSON'S RATIOS; SNAP-THROUGH INSTABILITY; STRUCTURAL BISTABILITY;

METAMATERIALS;

EID: 84995741439     PISSN: None     EISSN: 23524316     Source Type: Journal    
DOI: 10.1016/j.eml.2016.09.001     Document Type: Article

References (53)

1. [1] Lee, J.H., Singer, J.P., Thomas, E.L., Micro-/nanostructured mechanical metamaterials. Adv. Mater. 24 (2012), 4782–4810.
2. [2] Greaves, G.N., Greer, A.L., Lakes, R.S., Rouxel, T., Poisson's ratio and modern materials. Nat. Mater. 10 (2011), 823–837.
3. [3] Grima, J.N., Alderson, A., Evans, K.E., Auxetic behaviour from rotating rigid units. Phys. Status Solidi B 242 (2005), 561–575.
4. [4] Lakes, R., Wojciechowski, K.W., Negative compressibility, negative Poisson's ratio, and stability. Phys. Status Solidi B 245 (2008), 545–551.
5. [5] Lakes, R., Foam structures with a negative Poisson's ratio. Science 235 (1987), 1038–1040.
6. 2 from first-principles calculations. Nature 358 (1992), 222–224.
7. [7] Baughman, R., Shacklette, J., Zakhidov, A., Stafstrom, S., Negative Poisson's ratios as a common feature of cubic metals. Nature 392 (1988), 362–365.
8. [8] Ruzzene, M., Scarpa, F., Soranna, F., Wave beaming effects in two-dimensional cellular structures. Smart Mater. Struct. 12 (2003), 363–372.
9. [9] Gatt, R., Mizzi, L., Azzopardi, J.I., Azzopardi, K.M., Attard, D., Casha, A., Briffa, J., Grima, J.N., Hierarchical auxetic mechanical metamaterials. Sci. Rep., 5, 2015, 8395.
10. [10] 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 (2014), 2365–2370.
11. [11] Ali, M.N., Busfield, J.J.C., Rehman, I.U., Auxetic oesophageal stents: structure and mechanical properties. J. Mater. Sci. 25 (2014), 527–553.
12. [12] Schaeffer, M., Ruzzene, M., Wave propagation in reconfigurable magneto-elastic kagome lattice structures. Appl. Phys. Lett., 117, 2015, 194903.
13. [13] Evans, K.E., Anderson, A., Auxetic materials: functional materials and structures from lateral thinking!. Adv. Mater. 12 (2000), 617–628.
14. [14] Yang, W., Li, Z.M., Shi, W., Xie, B.H., Yang, M.B., Review on auxetic materials. J. Math. Sci. 39 (2004), 3269–3279.
15. [15] Alderson, A., Alderson, K.L., Auxetic materials. Proc. IMechE G: J. Aerosp. Eng. 221 (2007), 565–575.
16. [16] Prawoto, Y., Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson's ratio. Comput. Mater. Sci. 58 (2012), 140–153.
17. [17] Grima, J.N., Evans, K.E., Auxetic behavior from rotating squares. J. Mater. Sci. Lett. 19 (2000), 1563–1565.
18. [18] Prall, D., Lakes, R.S., Properties of a chiral honeycomb with a Poisson's ratio of -1. Int. J. Mech. Sci. 39 (1997), 305–314.
19. [19] Scarpa, F., Blain, S., Lew, T., Perrott, D., Ruzzene, M., Yates, J.R., Elastic buckling of hexagonal chiral cell honeycombs. Composites A 38 (2007), 280–289.
20. [20] Cabras, L., Brun, M., Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to -1. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 470, 2014, 20140538.
21. [21] Grima, J.N., Gatt, R., Perforated sheets exhibiting negative Poisson's ratios. Adv. Eng. Mater. 12 (2010), 460–464.
22. [22] Shan, S., Kang, S.H., Zhao, Z., Fang, L., Bertoldi, K., Design of planar isotropic negative Poisson's ratio structures. Extreme Mech. Lett. 4 (2015), 96–102.
23. [23] Grima, J.N., Mizzi, L., Azzopardi, K.M., Gatt, R., Auxetic perforated mechanical metamaterials with randomly oriented cuts. Adv. Mater. 28 (2015), 385–389.
24. [24] Cho, Y., Shin, J.-H., Costa, A., Kim, T.A., Kunin, V., Li, J., Yeon Lee, S., Yang, S., Han, H.N., Choi, I.-S., Srolovitz, D.J., Engineering the shape and structure of materials by fractal cut. Proc. Natl. Acad. Sci. USA 111 (2014), 17390–17395.
25. [25] Suzuki, Y., Cardone, G., Restrepo, D., Zavattieri, P.D., Baker, T.S., Tezcan, A.F., Self-assembly of coherently dynamic, auxetic, two-dimensional protein crystals. Nature 533 (2016), 369–373.
26. [26] Grima, J.N., Manicaro, E., Attard, D., Auxetic behaviour from connected different-sized squares and rectangles. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 467 (2011), 439–458.
27. [27] Silverberg, J.L., Evans, A.A., McLeod, L., Hayward, R.C., Hull, T., Santangelo, C.D., Cohen, I., Using origami design principles to fold reprogrammable mechanical metamaterials. Science 345 (2014), 647–650.
28. [28] Silverberg, J.L., Na, J.-H., Evans, A.A., Liu, B., Hull, T.C., Santangelo, C.D., Lang, R.J., Hayward, R.C., Cohen, I., Origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat. Mater. 14 (2015), 389–393.
29. [29] Dudte, L.H., Vouga, E., Tachi, T., Mahadevan, L., Programming curvature using origami tessellations. Nat. Mater. 15 (2016), 583–588.
30. [30] Shyu, T.C., Damasceno, P.F., Dodd, P.M., Lamoureux, A., Xu, L., Shlian, M., Shtein, M., Glotzer, S.C., Kotov, N.A., A kirigami approach to engineering elasticity in nanocomposites through patterned defects. Nat. Mater. 14 (2015), 785–790.
31. [31] Blees, M.K., Barnard, A.W., Rose, P.A., Roberts, S.P., McGill, K.L., Huang, P.Y., Ruyack, A.R., Kevek, J.W., Kobrin, B., Muller, D.A., McEuen, P.L., Graphene kirigami. Nature 524 (2015), 204–207.
32. [32] Eidini, M., Paulino, G.H., Unraveling metamaterial properties in zigzag-base folded sheets. Sci. Adv., 1, 2015, e1500224.
33. [33] Tachi, T., Designing freeform origami tessellations by generalizing Resch's patterns. ASME J. Mech. Des., 135, 2013, 111006.
34. [34] Schenk, M., Guest, S.D., Geometry of Miura-folded metamaterials. Proc. Natl. Acad. Sci. USA 110 (2013), 3276–3281.
35. [35] Eidini, M., Zigzag-base folded sheet cellular mechanical metamaterials. Extreme Mech. Lett. 6 (2016), 96–102.
36. [36] Bertoldi, K., Reis, P.M., Willshaw, S., Mullin, T., Negative Poisson's ratio behavior induced by an elastic instability. Adv. Mater. 22 (2010), 361–366.
37. [37] Overvelde, J.T.B., Shan, S., Bertoldi, K., Compaction through buckling in 2D periodic, soft and porous structures: effect of pore shape. Adv. Mater. 24 (2012), 2337–5049.
38. [38] Babaee, S., Shim, J., Weaver, J.C., Chen, E.R., Patel, N., Bertoldi, K., 3D soft metamaterials with negative Poisson's ratio. Adv. Mater. 25 (2013), 5044–5049.
39. [39] Wu, G., Cho, Y., Choi, I.-S., Ge, D., Li, J., Han, H.N., Lubensky, T., Yang, S., Directing the deformation paths of soft metamaterials with prescribed asymmetric units. Adv. Mater. 27 (2015), 2747–2752.
40. [40] Florijn, B., Coulais, C., van Hecke, M., Programmable mechanical metamaterials. Phys. Rev. Lett., 113, 2014, 175503.
41. [41] Qiu, J., Lang, H.L., Slocum, A.H., A curved-beam bistable mechanism. J. Microelectromech. Syst. 13 (2004), 137–146.
42. [42] Guest, S.D., Pellegrino, S., Analytical models for bistable cylindrical shells. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 462 (2006), 839–854.
43. [43] Pandey, A., Moulton, D.E., Vella, D., Holmes, D.P., Dynamics of snapping beams and jumping poppers. Europhys. Lett., 105, 2014, 24001.
44. [44] Yasuda, H., Yang, J., Reentrant origami-based metamaterials with negative Poisson's ratio and bistability. Phys. Rev. Lett., 114, 2015, 185502.
45. [45] Lu, P.J., Steinhardt, P.J., Decagonal and quasi-Crystalline tilings in medieval Islamic architecture. Science 315 (2007), 1106–1110.
46. [46] Seherr-Thoss, Sonia P., Design and Color in Islamic Architecture: Afghanistan, Iran, Turkey, Vol. 4741. 1968, Smithsonian Institution Press.
47. [47] Moore, B., Jaglinski, T., Stone, T.S., Lakes, R.S., Negative incremental bulk modulus in foams. Phil. Mag. Lett. 86 (2006), 651–659.
48. [48] Restrepo, D., Mankame, N.D., Zavattieri, P.D., Phase transforming cellular materials. Extreme Mech. Lett. 4 (2015), 52–60.
49. [49] 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 (2015), 5523–5527.
50. [50] Gjerde, E., Origami Tessellations: Awe-Inspiring Geometric Designs. 2008, Taylor and Francis, USA.
51. [51] Duoss, E.B., Weisgraber, T.H., Hearon, K., Zhu, C., Small, W. IV, Metz, T.R., Vericella, J.J., Barth, H.D., Kuntz, J.D., Maxwell, R.S., Spadaccini, C.M., Wilson, T.S., Three-dimensional printing of elastomeric, cellular architectures with negative stiffness. Adv. Funct. Mater. 24 (2014), 4905–4913.
52. [52] Shan, S., Kang, S.H., Raney, J.R., Wang, P., Fang, L., Candido, F., Lewis, J.A., Bertoldi, K., Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27 (2015), 4296–4301.
53. [53] Rafsanjani, A., Akbarzadeh, A., Pasini, D., Snapping mechanical metamaterials under tension. Adv. Mater. 27 (2015), 5931–5935.