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Multi-stable mechanical metamaterials by elastic buckling instability

Journal of Materials Science volume 54, pages 3509–3526 (2019)Cite this article

Abstract

The mechanical responses of two novel kinds of two-dimensional (2D) mechanical metamaterials containing opposite or parallel snapping curved (U-shaped) segments with elastic snap-through instability mechanism are systematically investigated. Under uniaxial loading, the metamaterials undergo a large deformation caused by stiffness mismatch between snapping (buckling instabilities) and supporting (relative stiffer/thicker) components, exhibiting very small transverse deformation after every snapping. Based on the multi-stable mechanism, phase transformation/shape-reconfiguration and zero Poisson’s ratio are achieved up to large morphological change. Nonlinear mechanical responses including self-recovering snapping and multi-stability enabling snapping behaviors can be generated by tuning the geometric parameters (the relative thickness of the snapping and supporting segments as well as the amplitude of the snapping curved segments). Then topology analysis is carried out to develop the 2D structures to a series of 3D hierarchical configurations from which can be chosen for various engineering conditions with enhanced snapping mechanism. Specifically, multi-stable/shape-reconfigurable tubes and cylinders are designed using the 3D configurations. Besides, one of the 3D metamaterials is developed for functional applications as shock absorber and damper, i.e., the process from fully stretched state to fully compacted state is used to absorb energy and reduce incoming pressure with small stiffness and strength; then the fully compacted metamaterials are used to carry load and attenuate vibration with relative bigger stiffness and strength. This work gives advance to the design, analysis and manufacture of functionally reconfigurable mechanical metamaterials.

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References

  1. Pendry JB, Schurig D, Smith DR (2006) Controlling electromagnetic fields. Science 312:1780–1782

    CAS  Article  Google Scholar 

  2. Schurig D, Mock JJ, Justice BJ, Cummer SA, Pendry JB, Starr AF, Smith DR (2006) Metamaterial electromagnetic cloak at microwave frequencies. Science 314:977–980

    CAS  Article  Google Scholar 

  3. Wegener M (2013) Metamaterials beyond optics. Science 342:939–940

    CAS  Article  Google Scholar 

  4. Maldovan M (2013) Sound and heat revolutions in phononics. Nature 503:209–217

    CAS  Article  Google Scholar 

  5. Bückmann T, Thiel M, Kadic M, Schittny R, Wegener M (2014) An elasto-mechanical unfeelability cloak made of pentamode metamaterials. Nat Commun 5:1–6

    Article  Google Scholar 

  6. Xu C, Stiubianu GT, Gorodetsky AA (2018) Adaptive infrared-reflecting systems inspired by cephalopods. Science 359:1495–1500

    CAS  Article  Google Scholar 

  7. Wang Q, Jackson JA, Ge Q, Hopkins JB, Spadaccini CM, Fang NX (2016) Lightweight mechanical metamaterials with tunable negative thermal expansion. Phys Rev Lett 117:175901

    Article  Google Scholar 

  8. Boatti E, Vasios N, Bertoldi K (2017) Origami metamaterials for tunable thermal expansion. Adv Mater 29:1700360

    Article  Google Scholar 

  9. Xu H, Farag A, Pasini D (2018) Routes to program thermal expansion in three-dimensional lattice metamaterials built from tetrahedral building blocks. J Mech Phys Solids 117:54–87

    Article  Google Scholar 

  10. Schaedler TA, Jacobsen AJ, Torrents A, Sorensen AE, Lian J, Greer JR, Valdevit L, Carter WB (2011) Ultralight metallic microlattices. Science 334:962–965

    CAS  Article  Google Scholar 

  11. Zheng X, Lee H, Weisgraber TH et al (2014) Ultralight, ultrastiff mechanical metamaterials. Science 344:1373–1377

    CAS  Article  Google Scholar 

  12. Meza LR, Das S, Greer JR (2014) Strong, lightweight, and recoverable three-dimensional ceramic nanolattices. Science 345:1322–1326

    CAS  Article  Google Scholar 

  13. Bauer J, Schroer A, Schwaiger R, Kraft O (2016) Approaching theoretical strength in glassy carbon nanolattices. Nat Mater 15:438–443

    CAS  Article  Google Scholar 

  14. Hou X, Silberschmidt VV (2015) Metamaterials with negative Poisson’s ratio: a review of mechanical properties and deformation mechanisms. In: Silberschmidt VV, Matveenko VP (eds) Mechanics of advanced materials. Springer, Cham, pp 155–179

    Google Scholar 

  15. Yu X, Zhou J, Liang H, Jiang Z, Wu L (2018) Mechanical metamaterials associated with stiffness, rigidity and compressibility: a brief review. Prog Mater Sci 94:114–173

    Article  Google Scholar 

  16. Rafsanjani A, Akbarzadeh A, Pasini D (2015) Snapping mechanical metamaterials under tension. Adv Mater 27:5931–5935

    CAS  Article  Google Scholar 

  17. Frenzel T, Findeisen C, Kadic M, Gumbsch P, Wegener M (2016) Tailored buckling microlattices as reusable light-weight shock absorbers. Adv Mater 28:5865–5870

    CAS  Article  Google Scholar 

  18. Ha CS, Lakes RS, Plesha ME (2018) Design, fabrication, and analysis of lattice exhibiting energy absorption via snap-through behavior. Mater Design 141:426–437

    Article  Google Scholar 

  19. Shan S, Kang SH, Raney JR, Wang P, Fang L, Candido F, Lewis JA, Bertoldi K (2015) Multistable architected materials for trapping elastic strain energy. Adv Mater 27:4296–4301

    CAS  Article  Google Scholar 

  20. Restrepo D, Mankame ND, Zavattieri PD (2015) Phase transforming cellular materials. Extreme Mech Lett 4:52–60

    Article  Google Scholar 

  21. Haghpanah B, Salari-Sharif L, Pourrajab P, Hopkins J, Valdevit L (2016) Multistable shape-reconfigurable architected materials. Adv Mater 28:7915–7920

    CAS  Article  Google Scholar 

  22. Yang H, Ma L (2018) Multi-stable mechanical metamaterials with shape-reconfiguration and zero Poisson’s ratio. Mater Design 152:181–190

    Article  Google Scholar 

  23. Che K, Yuan C, Wu J, Qi HJ, Meaud J (2017) Three-dimensional-printed multistable mechanical metamaterials with a deterministic deformation sequence. J Appl Mech 84:011004

    Article  Google Scholar 

  24. Lakes RS, Lee T, Bersie A, Wang YC (2001) Extreme damping in composite materials with negative-stiffness inclusions. Nature 410:565–567

    CAS  Article  Google Scholar 

  25. Barbarino S, Flores ES, Ajaj RM, Dayyani I, Friswell MI (2014) A review on shape memory alloys with applications to morphing aircraft. Smart Mater Struct 23:063001

    Article  Google Scholar 

  26. Felton SM, Tolley MT, Shin B, Onal CD, Demaine ED, Rus D, Wood RJ (2013) Self-folding with shape memory composites. Soft Matter 9:7688–7694

    CAS  Article  Google Scholar 

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

    Article  Google Scholar 

  28. Hewage TA, Alderson KL, Alderson A, Scarpa F (2016) Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative Poisson’s ratio properties. Adv Mater 28:10323–10332

    CAS  Article  Google Scholar 

  29. Overvelde JTB, Weaver JC, Hoberman C, Bertoldi K (2017) Rational design of reconfigurable prismatic architected materials. Nature 541:347–352

    CAS  Article  Google Scholar 

  30. Bauer J, Hengsbach S, Tesari I, Schwaiger R, Kraft O (2014) High-strength cellular ceramic composites with 3D microarchitecture. PNAS 111:2453–2458

    CAS  Article  Google Scholar 

  31. Holmes DP, Crosby AJ (2007) Snapping surfaces. Adv Mater 19:3589–3593

    CAS  Article  Google Scholar 

  32. Guo Q, Zheng H, Chen Z (2014) Modeling bistable behaviors in morphing structures through finite element simulations. Bio-Med Mater Eng 24:557–562

    Google Scholar 

  33. Silverberg JL, Na J, Evans AA et al (2015) Corrigendum: origami structures with a critical transition to bistability arising from hidden degrees of freedom. Nat Mater 14:389–393

    CAS  Article  Google Scholar 

  34. Florijn B, Coulais C, Hecke MV (2014) Programmable mechanical metamaterials. Phys Rev Lett 113:175503

    Article  Google Scholar 

  35. Silverberg JL, Evans AA, McLeod L, Hayward RC, Hull T, Santangelo CD, Cohen I (2014) Applied origami. Using origami design principles to fold reprogrammable mechanical metamaterials. Science 345:647–649

    CAS  Article  Google Scholar 

  36. Fu H, Nan K, Bai W et al (2018) Morphable 3D mesostructures and microelectronic devices by multistable buckling mechanics. Nat Mater 17:268–276

    CAS  Article  Google Scholar 

  37. Milton GW (2013) Complete characterization of the macroscopic deformations of periodic unimode metamaterials of rigid bars and pivots. J Mech Phys Solids 61:1543–1560

    Article  Google Scholar 

  38. Moore B, Jaglinski T, Stone DS, Lakes RS (2006) Negative incremental bulk modulus in foams. Philos Mag Lett 86:651–659

    CAS  Article  Google Scholar 

  39. Puglisi G, Truskinovsky L (2000) Mechanics of a discrete chain with bi-stable elements. J Mech Phys Solids 48:1–27

    Article  Google Scholar 

  40. Jaglinski T, Frascone P, Moore B, Stone DS, Lakes RS (2006) Internal friction due to negative stiffness in the indium-thallium martensitic phase transformation. Phil Mag 86:4285–4303

    CAS  Article  Google Scholar 

  41. Qiu J, Lang JH, Slocum AH (2004) A curved-beam bistable mechanism. J Microelectromech Syst 13:137–146

    Article  Google Scholar 

  42. Findeisen C, Hohe J, Kadic M, Gumbsch P (2017) Characteristics of mechanical metamaterials based on buckling elements. J Mech Phys Solids 102:151–164

    Article  Google Scholar 

  43. Yi J, Boyce MC, Lee GF, Balizer E (2006) Large deformation rate-dependent stress–strain behavior of polyurea and polyurethanes. Polymer 47:319–329

    CAS  Article  Google Scholar 

  44. Bertoldi K, Boyce MC (2008) Mechanically triggered transformations of phononic band gaps in periodic elastomeric structures. Phys Rev B 77:052105

    Article  Google Scholar 

  45. Yu K, Fang NX, Huang G, Wang Q (2018) Magnetoactive acoustic metamaterials. Adv Mater 30:1706348

    Article  Google Scholar 

  46. Banerjee A, Bernoulli D, Zhang H et al (2018) Ultralarge elastic deformation of nanoscale diamond. Science 360:300–302

    CAS  Article  Google Scholar 

Download references

Acknowledgements

The present work is supported by National Natural Science Foundation of China under Grant No. 11672085.

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Authors and Affiliations

  1. Center for Composite Materials, Harbin Institute of Technology, Harbin, 150080, People’s Republic of China

    Hang Yang & Li Ma

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  1. Hang Yang
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  2. Li Ma
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Correspondence to Li Ma.

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Yang, H., Ma, L. Multi-stable mechanical metamaterials by elastic buckling instability. J Mater Sci 54, 3509–3526 (2019). https://doi.org/10.1007/s10853-018-3065-y

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  • DOI: https://doi.org/10.1007/s10853-018-3065-y

Keywords

  • Mechanical Metamaterials
  • Buckling Instability
  • Crack Curving
  • Snap-through Instability
  • Large Morphological Changes