Advertisement

Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization

  • 1195 Accesses

  • 11 Citations

Abstract

A novel design concept for buckling-induced mechanical metamaterials for energy absorption is presented. The force-displacement curves of the mechanical metamaterials are analyzed according to the curves of their unit cells, and the energy-absorbing characteristics of mechanical metamaterials are evaluated. Two topology optimization models are proposed. One maximizes the buckling-induced dissipated energy to facilitate the design of metamaterials with high energy absorption and low elastic strain energy. The other maximizes the dissipated energy with a constraint that the mechanical metamaterials should be self-recoverable. An energy interpolation scheme is employed to avoid numerical instabilities in the geometric nonlinear finite element analysis. A two-phase algorithm is proposed to find the optimized result from a uniform initial guess, and sensitivity analysis is performed. The optimized design has a larger amount of buckling-induced dissipated energy than the previously proposed structural prototypes. Moreover, the self-recoverable mechanical metamaterial is successfully designed by topology optimization.

This is a preview of subscription content, log in to check access.

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 199

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

References

  1. Bochenek B, Tajs-Zielińska K (2015) Minimal compliance topologies for maximal buckling load of columns. Struct Multidiscip Optim 51(5):1149–1157

  2. Bruns TE, Sigmund O (2004) Toward the topology design of mechanisms that exhibit snap-through behavior. Comput Methods Appl Mech Eng 193(36):3973–4000

  3. Bruns TE, Sigmund O, Tortorelli DA (2002) Numerical methods for the topology optimization of structures that exhibit snap-through. Int J Numer Methods Eng 55(10):1215–1237

  4. Bruyneel M, Duysinx P, Fleury C (2002) A family of mma approximations for structural optimization. Struct Multidiscip Optim 24(4):263–276

  5. 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(1):011004

  6. Correa DM, Klatt T, Cortes S, Haberman M, Kovar D, Seepersad C (2015) Negative stiffness honeycombs for recoverable shock isolation. Rapid Prototyp J 21(2):193–200

  7. Costas M, Díaz J, Romera L, Hernández S (2014) A multi-objective surrogate-based optimization of the crashworthiness of a hybrid impact absorber. Int J Mech Sci 88:46–54

  8. Deepak SR, Dinesh M, Sahu DK, Ananthasuresh GK (2009) A comparative study of the formulations and benchmark problems for the topology optimization of compliant mechanisms. J Mech Robot 1(1):011003

  9. Dunning PD, Ovtchinnikov E, Scott J, Alicia Kim H (2016) Level-set topology optimization with many linear buckling constraints using an efficient and robust eigensolver. Int J Numer Methods Eng 107:1029–1053

  10. Evans AG, He MY, Deshpande VS, Hutchinson JW, Jacobsen AJ, Carter WB (2010) Concepts for enhanced energy absorption using hollow micro-lattices. Int J Impact Eng 37(9):947–959

  11. Fang J, Sun G, Na Q, Kim NH, Li Q (2016) On design optimization for structural crashworthiness and its state of the art. Struct Multidiscip Optim 55:1–29

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

  13. Forsberg J, Nilsson L (2007) Topology optimization in crashworthiness design. Struct Multidiscip Optim 33(1):1–12

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

  15. Gao X, Ma H (2015) Topology optimization of continuum structures under buckling constraints. Comput Struct 157:142–152

  16. Gatt R, Mizzi L, Azzopardi JI, Azzopardi KM, Attard D, Casha A, Briffa J, Grima JN (2015) Hierarchical auxetic mechanical metamaterials. Sci Rep 5:8395

  17. Haghpanah B, Salari-Sharif L, Pourrajab P, Hopkins J, Valdevit L (2016) Multistable shape-reconfigurable architected materials. Adv Mater 28(36):7915–7920

  18. He G, Huang X, Hu W, Li G (2016) Topology optimization of periodic structures using beso based on unstructured design points. Struct Multidiscip Optim 53(2):271–275

  19. Hu N, Burgueño R (2015) Buckling-induced smart applications: recent advances and trends. Smart Mater Struct 24(6):063001

  20. James KA, Waisman H (2016) Layout design of a bi-stable cardiovascular stent using topology optimization. Comput Methods Appl Mech Eng 305:869–890

  21. Kawamoto A (2009) Stabilization of geometrically nonlinear topology optimization by the levenberg–marquardt method. Struct Multidiscip Optim 37(4):429–433

  22. Kiani M, Motoyama K, Rais-Rohani M, Shiozaki H (2014) Joint stiffness analysis and optimization as a mechanism for improving the structural design and performance of a vehicle. Proceedings of the Institution of Mechanical Engineers Part D Journal of Automobile Engineering 228(6):689–700

  23. Kim JJ, Jang IG (2016) Image resolution enhancement for healthy weight-bearing bones based on topology optimization. J Biomech 49(13):3035–3040

  24. Lahuerta RD, Simões ET, Campello EMB, Pimenta PM, Silva ECN (2013) Towards the stabilization of the low density elements in topology optimization with large deformation. Comput Mech 52(4):779–797

  25. Lee H-A, Park G-J (2012) Topology optimization for structures with nonlinear behavior using the equivalent static loads method. J Mech Des 134(3):031004

  26. Lee J-H, Wang L, Kooi S, Boyce MC, Thomas EL (2010) Enhanced energy dissipation in periodic epoxy nanoframes. Nano Lett 10(7):2592–2597

  27. Lee J-H, Singer JP, Thomas EL (2012) Micro-/nanostructured mechanical metamaterials. Adv Mater 24(36):4782–4810

  28. Li L, Zhang G, Khandelwal K (2017) Topology optimization of energy absorbing structures with maximum damage constraint. Int J Numer Methods Eng 112:737–775

  29. Lindgaard E, Dahl J (2013) On compliance and buckling objective functions in topology optimization of snap-through problems. Struct Multidiscip Optim 47(3):409–421

  30. Liu M, Zhang X, Fatikow S (2017) Design and analysis of a multi-notched flexure hinge for compliant mechanisms. Precis Eng 48:292–304

  31. Luo Q, Tong L (2015) Structural topology optimization for maximum linear buckling loads by using a moving iso-surface threshold method. Struct Multidiscip Optim 52(1):71–90

  32. Luo Q, Tong L (2016) An algorithm for eradicating the effects of void elements on structural topology optimization for nonlinear compliance. Struct Multidiscip Optim 53(4):695–714

  33. Mayer RR, Kikuchi N, Scott RA (1996) Application of topological optimization techniques to structural crashworthiness. Int J Numer Methods Eng 39(8):1383–1403

  34. Mohammadiha O, Beheshti H (2014) Optimization of functionally graded foam-filled conical tubes under axial impact loading. J Mech Sci Technol 28(5):1741–1752

  35. Nicolaou ZG, Motter AE (2012) Mechanical metamaterials with negative compressibility transitions. Nat Mater 11(7):608–613

  36. Patel NM, Kang B-S, Renaud JE, Tovar A (2009) Crashworthiness design using topology optimization. J Mech Des 131(6):061013

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

  38. Rafsanjani A, Akbarzadeh A, Pasini D (2015) Snapping mechanical metamaterials under tension. Adv Mater 27(39):5931–5935

  39. Rojas-Labanda S, Stolpe M (2015) Automatic penalty continuation in structural topology optimization. Struct Multidiscip Optim 52(6):1205–1221

  40. 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(29):4296–4301

  41. Sigmund O, Maute K (2013) Topology optimization approaches. Struct Multidiscip Optim 48(6):1031–1055

  42. Tran AV, Zhang X, Zhu B (2017) The development of a new piezoresistive pressure sensor for low pressure. IEEE Trans Ind Electron PP(99):1–1

  43. van Dijk NP, Langelaar M, van Keulen F (2014) Element deformation scaling for robust geometrically nonlinear analyses in topology optimization. Struct Multidiscip Optim 50(4):537–560

  44. Wang R, Zhang X (2018) Parameters optimization and experiment of a planar parallel 3-dof nanopositioning system. IEEE Trans Ind Electron 65(3):2388–2397

  45. Wang F, Lazarov BS, Sigmund O (2011) On projection methods, convergence and robust formulations in topology optimization. Struct Multidiscip Optim 43(6):767–784

  46. Wang F, Sigmund O, Jensen JS (2014a) Design of materials with prescribed nonlinear properties. J Mech Phys Solids 69:156– 174

  47. Wang F, Lazarov BS, Sigmund O, Jensen JS (2014b) Interpolation scheme for fictitious domain techniques and topology optimization of finite strain elastic problems. Comput Methods Appl Mech Eng 276:453–472

  48. Yoon GH, Kim YY (2005) Element connectivity parameterization for topology optimization of geometrically nonlinear structures. Int J Solids Struct 42(7):1983–2009

  49. Zheng X, Lee H, Weisgraber TH, Shusteff M, DeOtte J, Duoss EB, Kuntz JD, Biener MM, Ge Q, Jackson JA et al (2014) Ultralight, ultrastiff mechanical metamaterials. Science 344(6190):1373–1377

  50. Zheng X, Smith W, Jackson J, Moran B, Cui H, Chen D, Ye J, Fang N, Rodriguez N, Weisgraber T et al (2016) Multiscale metallic metamaterials. Nat Mater 15:1100–1106

  51. Zhu B, Zhang X, Fatikow S (2015) Structural topology and shape optimization using a level set method with distance-suppression scheme. Comput Methods Appl Mech Eng 283:1214–1239

Download references

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. U1501247 and U1609206). This support is greatly appreciated. Additionally, the authors thank Dr. K. Svanberg at KTH (Stockholm, Sweden) for providing the MMA code for academic research.

Author information

Correspondence to Xianmin Zhang.

Ethics declarations

Conflict of interests

The authors declare that they have no conflicts of interest.

Additional information

Publisher’s Note

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

Responsible Editor: Kurt Maute

Electronic supplementary material

Below is the link to the electronic supplementary material.

(AVI 399 KB)

(AVI 429 KB)

(AVI 451 KB)

(AVI 720 KB)

(AVI 399 KB)

(AVI 429 KB)

(AVI 451 KB)

(AVI 720 KB)

(AVI 15.7 MB)

(AVI 17.6 MB)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Chen, Q., Zhang, X. & Zhu, B. Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization. Struct Multidisc Optim 58, 1395–1410 (2018) doi:10.1007/s00158-018-1970-y

Download citation

Keywords

  • Mechanical metamaterial
  • Energy absorption
  • Topology optimization
  • Buckling