Mechanical instabilities are traditionally regarded as a route toward failure. However, they can also be exploited to design architected cellular materials with tunable functionality. In this review, we focus on three examples and show that mechanical instabilities in architected cellular materials can be harnessed () to design auxetic materials, () to control the propagation of elastic waves, and () to realize reusable energy-absorbing materials. Together, these examples highlight a new strategy to design tunable systems across a wide range of length scales.


Article metrics loading...

Loading full text...

Full text loading...


Literature Cited

  1. Gibson LJ, Ashby MF. 1.  1999. Cellular Solids: Structure and Properties Cambridge, UK: Cambridge Univ. Press [Google Scholar]
  2. Schaedler TA, Jacobsen AJ, Torrents A, Sorensen AE, Lian J. 2.  et al. 2011. Ultralight metallic microlattices. Science 334:962–65 [Google Scholar]
  3. Lee J-H, Wang L, Boyce MC, Thomas EL. 3.  2012. Periodic bicontinuous composites for high specific energy absorption. Nano Lett. 12:84392–96 [Google Scholar]
  4. Maldovan M, Thomas EL. 4.  2009. Periodic Materials and Interference Lithography for Photonics, Phononics and Mechanics Weinheim, Ger.: Wiley-VCH [Google Scholar]
  5. Zheng X, Lee H, Weisgraber TH, Shusteff M, DeOtte J. 5.  et al. 2014. Ultralight, ultrastiff mechanical metamaterials. Science 344:61901373–77 [Google Scholar]
  6. Meza LR, Das S, Greer JR. 6.  2014. Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345:62021322–26 [Google Scholar]
  7. Bauer J, Hengsbach S, Tesari I, Schwaiger R, Kraft O. 7.  2014. High-strength cellular ceramic composites with 3D microarchitecture. PNAS 111:72453–58 [Google Scholar]
  8. Meza LR, Zelhofer AJ, Clarke N, Mateos AJ, Kochmann DM, Greer JR. 8.  2015. Resilient 3D hierarchical architected metamaterials. PNAS 112:3711502–7 [Google Scholar]
  9. Leong TG, Randall CL, Benson BR, Bassik N, Stern GM, Gracias DH. 9.  2009. Tetherless thermobiochemically actuated microgrippers. PNAS 106:3703–8 [Google Scholar]
  10. Liu Y, Boyles JK, Genzer J, Dickey MD. 10.  2012. Self-folding of polymer sheets using local light absorption. Soft Matter 8:1764–69 [Google Scholar]
  11. Laflin KE, Morris CJ, Muqeem T, Gracias DH. 11.  2012. Laser triggered sequential folding of microstructures. Appl. Phys. Lett. 101:131901 [Google Scholar]
  12. Shenoy VB, Gracias DH. 12.  2012. Self-folding thin-film materials: from nanopolyhedra to graphene origami. MRS Bull. 37:847–54 [Google Scholar]
  13. Cho J-H, Keung MD, Verellen N, Lagae L, Moshchalkov VV. 13.  et al. 2011. Nanoscale origami for 3D optics. Small 7:141943–48 [Google Scholar]
  14. Xu S, Yan Z, Jang K-I, Huang W, Fu H. 14.  et al. 2015. Assembly of micro/nanomaterials into complex, three-dimensional architectures by compressive buckling. Science 347:6218154–59 [Google Scholar]
  15. Kim J, Hanna JA, Byun M, Santangelo CD, Hayward RC. 15.  2012. Designing responsive buckled surfaces by halftone gel lithography. Science 335:60731201–5 [Google Scholar]
  16. Osanov M, Guest JK. 16.  2016. Topology optimization for architected materials design. Annu. Rev. Mater. Res. 46:211–33 [Google Scholar]
  17. Mullin T, Deschanel S, Bertoldi K, Boyce MC. 17.  2007. Pattern transformation triggered by deformation. Phys. Rev. Lett. 99:084301 [Google Scholar]
  18. Zhang Y, Matsumoto EA, Peter A, Lin PC, Kamien RD, Yang S. 18.  2008. One-step nanoscale assembly of complex structures via harnessing of an elastic instability. Nano Lett. 8:1192–96 [Google Scholar]
  19. Bertoldi K, Reis PM, Willshaw S, Mullin T. 19.  2010. Negative Poisson's ratio behavior induced by an elastic instability. Adv. Mater. 22:361–66 [Google Scholar]
  20. Shim J, Perdigou C, Chen ER, Bertoldi K, Reis PM. 20.  2012. Buckling-induced encapsulation of structured elastic shells under pressure. PNAS 109:5978–83 [Google Scholar]
  21. Lakes RS.21.  1987. Foam structures with a negative Poisson's ratio. Science 235:1038–40 [Google Scholar]
  22. Milton G.22.  1992. Composite materials with Poisson's ratio close to −1. J. Mech. Phys. Solids 40:1105–37 [Google Scholar]
  23. Friis EA, Lakes RS, Park JB. 23.  1988. Negative Poisson's ratio polymeric and metallic materials. J. Mater. Sci. 23:4406–14 [Google Scholar]
  24. Caddock BD, Evans KE. 24.  1998. Microporous materials with negative Poisson's ratio. I. Microstructure and mechanical properties. J. Phys. D Appl. Phys. 22:1877 [Google Scholar]
  25. Evans KE, Nkansah MK, Hutchison IJ, Rogers SC. 25.  1991. Molecular network design. Nature 353:124–24 [Google Scholar]
  26. Rechtsman MC, Stillinger FH, Torquato S. 26.  2008. Negative Poisson's ratio materials via isotropic interactions. Phys Rev. Lett. 101:085501 [Google Scholar]
  27. Grima JN, Alderson A, Evans KE. 27.  2005. Auxetic behaviour from rotating rigid units. Phys. Stat. Solid. B 242:561–57 [Google Scholar]
  28. Shim J, Shan S, Kosmrlj A, Kang SH, Chen ER. 28.  et al. 2013. Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials. Soft Matter 9:8198–202 [Google Scholar]
  29. Overvelde JTB, Shan S, Bertoldi K. 29.  2012. Compaction through buckling in 2D periodic, soft and porous structures: effect of pore shape. Adv. Mater. 24:2337–42 [Google Scholar]
  30. Babaee S, Shim J, Weaver JC, Patel N, Bertoldi K. 30.  2013. 3D soft metamaterials with negative Poisson's ratio. Adv. Mater. 25:5044–49 [Google Scholar]
  31. Shen J, Zhou S, Huang X, Xie YM. 31.  2014. Simple cubic three-dimensional auxetic metamaterials. Phys. Status Solid. B 251:1515–22 [Google Scholar]
  32. Hussein M, Leamy M, Ruzzene M. 32.  2014. Dynamics of phononic materials and structures: historical origins, recent progress and future outlook. Appl. Mech. Rev. 66:040802 [Google Scholar]
  33. Khelif A, Choujaa A, Benchabane S, Djafari-Rouhani B, Laude V. 33.  2004. Guiding and bending of acoustic waves in highly confined phononic crystal waveguides. Appl. Phys. Lett. 84:224400–2 [Google Scholar]
  34. Kafesaki M, Sigalas MM, Garcia N. 34.  2000. Frequency modulation in the transmittivity of wave guides in elastic-wave band-gap materials. Phys. Rev. Lett. 85:4044–47 [Google Scholar]
  35. Cummer SA, Schurig D. 35.  2007. One path to acoustic cloaking. New J. Phys. 9:45 [Google Scholar]
  36. Elser D, Andersen UL, Korn A, Glöckl O, Lorenz S. 36.  et al. 2006. Reduction of guided acoustic wave Brillouin scattering in photonic crystal fibers. Phys. Rev. Lett. 97:133901 [Google Scholar]
  37. Elnady T, Elsabbagh A, Akl W, Mohamady O, Garcia-Chocano VM. 37.  et al. 2009. Quenching of acoustic bandgaps by flow noise. Appl. Phys. Lett. 94:13134104 [Google Scholar]
  38. Casadei F, Dozio L, Ruzzene M, Cunefare K. 38.  2010. Periodic shunted arrays for the control of noise radiation in an enclosure. J. Sound Vib. 329:3632 [Google Scholar]
  39. Airoldi L, Ruzzene M. 39.  2011. Design of tunable acoustic metamaterials through periodic arrays of resonant shunted piezos. New J. Phys. 13:11113010 [Google Scholar]
  40. Casadei F, Beck B, Cunefare KA, Ruzzene M. 40.  2012. Vibration control of plates through hybrid configurations of periodic piezoelectric shunts. Int. J. Solids Struct. 23:1169 [Google Scholar]
  41. Kittel C.41.  1967. Introduction to solid state physics. Am. J. Phys. 35:547–48 [Google Scholar]
  42. Liu Z, Zhang X, Mao Y, Zhu YY, Yang Z. 42.  et al. 2000. Locally resonant sonic materials. Science 289:54851734–36 [Google Scholar]
  43. Vikram KK, Eric L. 43.  1983. An experimental investigation of pass bands and stop bands in two periodic particulate composites. Int. J. Solids Struct. 19:5393–410 [Google Scholar]
  44. Kafesaki M, Sigalas MM, Economou EN. 44.  1995. Elastic wave band gaps in 3-D periodic polymer matrix composites. Solid State Commun. 96:285–89 [Google Scholar]
  45. Zhang X, Liu Z, Liu Y, Wu F. 45.  2003. Elastic wave band gaps for three-dimensional phononic crystals with two structural units. Phys. Lett. A 313:5–6455–60 [Google Scholar]
  46. Page JH, Yang S, Cowan ML, Liu Z, Chan CT, Sheng P. 46.  2003. 3D phononic crystals. Wave Scattering in Complex Media: From Theory to Applications (NATO Science Series, Vol. 107) BA van Tiggelen, SE Skipetrov 282–307 Netherlands: Springer [Google Scholar]
  47. Yang SX, Page JH, Liu ZY, Cowan ML, Chan CT, Sheng P. 47.  2004. Focusing of sound in a 3D phononic crystal. Phys. Rev. Lett. 93:024301 [Google Scholar]
  48. Sainidou R, Djafari-Rouhani B, Pennec Y, Vasseur JO. 48.  2006. Locally resonant phononic crystals made of hollow spheres or cylinders. Phys. Rev. B 73:024302 [Google Scholar]
  49. Daraio C.49.  2006. Design of materials configurations for enhanced phononic and electronic properties PhD thesis, Univ. Calif., San Diego [Google Scholar]
  50. Wang L, Bertoldi K. 50.  2012. Mechanically tunable phononic band gaps in three-dimensional periodic elastomeric structures. Int. J. Solids Struct. 49:19–202881–85 [Google Scholar]
  51. Jang JH, Ullal CK, Tsukruk VV, Thomas EL. 51.  2006. Mechanically tunable three dimensional elastomeric network/air structures via interference lithography. Nano Lett. 6:740–43 [Google Scholar]
  52. Bertoldi K, Boyce MC. 52.  2008. Mechanically-triggered transformations of phononic band gaps in periodic elastomeric structures. Phys. Rev. B 77:052105 [Google Scholar]
  53. Wang P, Shim J, Bertoldi K. 53.  2013. Effects of geometric and material non-linearities on the tunable response of phononic crystals. Phys. Rev. B 88:014304 [Google Scholar]
  54. Pal RK, Rimoli J, Ruzzene M. 54.  2016. Effect of large deformation pre-loads on the wave properties of hexagonal lattices. Smart Mater. Struct. 25:054010 [Google Scholar]
  55. Mousanezhad D, Babaee S, Ghosh R, Mahdi E, Bertoldi K, Vaziri A. 55.  2015. Honeycomb phononic crystals with self-similar hierarchy. Phys. Rev. B 92:104304 [Google Scholar]
  56. Rudykh S, Boyce MC. 56.  2014. Transforming wave propagation in layered media via instability-induced wrinkling interfacial layer. Phys. Rev. Lett. 112:034301 [Google Scholar]
  57. Wang P, Casadei F, Shan S, Weaver JC, Bertoldi K. 57.  2014. Harnessing buckling to design tunable locally resonant acoustic metamaterials. Phys. Rev. Lett. 113:014301 [Google Scholar]
  58. Celli P, Gonella S, Tajeddini V, Muliana A, Ahmed S, Ounaies Z. 58.  2016. Wave control through soft microstructural curling: bandgap shifting, reconfigurable anisotropy and switchable chirality. arXiv:1609.08404 [cond-mat.soft]
  59. Babaee S, Wang P, Bertoldi K. 59.  2015. Three-dimensional adaptive soft phononic crystals. J. Appl. Phys. 117:244903 [Google Scholar]
  60. Shan S, Kang SH, Wang P, Qu C, Shian S. 60.  et al. 2014. Harnessing multiple folding mechanisms in soft periodic structures for tunable control of elastic waves. Adv. Funct. Mater. 24:4935 [Google Scholar]
  61. Singamaneni S, Bertoldi K, Chang S, Jang JH, Thomas EL. 61.  et al. 2009. Instabilities and pattern transformation in periodic, porous elastoplastic solid coatings. Appl. Mater. Interfaces 1:42–47 [Google Scholar]
  62. Li J, Shim J, Deng J, Overvelde JTB, Bertoldi X. 62.  et al. 2012. Switching periodic membranes via pattern transformation and shape memory effect. Soft Matter 8:10322–28 [Google Scholar]
  63. Papka SD, Kyriakides S. 63.  1994. In-plane compressive response and crushing of honeycomb. J. Mech. Phys. Solids 42:1499–532 [Google Scholar]
  64. Pugsley A, Macaulay M. 64.  1960. The large-scale crumpling of thin cylindrical columns. Q. J. Mech. Appl. Math. 13:1–9 [Google Scholar]
  65. Reid SR.65.  1993. Plastic deformation mechanisms in axially compressed metal tubes used as impact energy absorbers. Int. J. Mech. Sci. 35:1035–52 [Google Scholar]
  66. Tattersall HG, Tappin G. 66.  1966. The work of fracture and its measurement in metals, ceramics and other materials. J. Mater. Sci. 1:296–301 [Google Scholar]
  67. Dawson MA, McKinley GH, Gibson LJ. 67.  2008. The dynamic compressive response of open-cell foam impregnated with a newtonian fluid. J. Appl. Mech. 75:041015 [Google Scholar]
  68. Gong L, Kyriakides S, Jang W-Y. 68.  2005. Compressive response of open-cell foams. I. Morphology and elastic properties. Int. J. Solids Struct. 42:5–61355–79 [Google Scholar]
  69. Florijn B, Coulais C, van Hecke M. 69.  2014. Programmable mechanical metamaterials. Phys. Rev. Lett. 113:175503 [Google Scholar]
  70. Correa DM, Klatt T, Cortes S, Haberman M, Kovar D, Seepersad C. 70.  2015. Negative stiffness honeycombs for recoverable shock isolation. Rapid Prototyping J. 21:193–200 [Google Scholar]
  71. Salari-Sharif L, Schaedler TA, Valdevit L. 71.  2014. Energy dissipation mechanisms in hollow metallic microlattices. J. Mater. Res. 29:1755–70 [Google Scholar]
  72. Shan S, Kang SH, Raney J, Wang P, Fang L. 72.  et al. 2015. Multistable architected materials for trapping elastic strain energy. Adv. Mater. 27:4296 [Google Scholar]
  73. Restrepo D, Mankame ND, Zavattieri PD. 73.  2015. Phase transforming cellular materials. Extreme Mech. Lett. 4:52–60 [Google Scholar]
  74. Haghpanah B, Salari-Sharif L, Pourrajab P, Hopkins J, Valdevit L. 74.  2016. Multistable shape-reconfigurable architected materials. Adv. Mater. 28:367915–20 [Google Scholar]

Data & Media loading...

  • Article Type: Review Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error