Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

A ready-to-manufacture optimization design of 3D chiral auxetics for additive manufacturing

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

The 3D chiral-type auxetic metamaterials have attracted massive attention in both academia and engineering. However, the complex deformation mechanism makes this kind of metamaterial hard to be topologically devised, especially in the 3D scenario. Most of existed studies only dealt with the re-entrant auxetics, and the optimized results are not able to be fabricated directly. This paper proposes a topology optimization design method for the 3D chiral-type auxetic metamaterial with ready-to-manufacture features. In this method, the matrix-compressed parametric level set is used to implicitly describe the high-resolution design boundary for the auxetic. In particular, the Gaussian radial basis function with global support is employed to parameterize the level set, and a discrete wavelet transform scheme is incorporated into the parametrization framework to effectively compress the full interpolation matrix. In this way, the optimization cost in 3D is noticeably reduced under a high numerical accuracy. To induce rotational deformation, rotation symmetry is applied to the micro-structured unit cell. The optimized microstructures possess explicit and smooth boundaries, and thus they can be 3D printed without tedious post-processing. Several 3D metallic microstructures with different Poisson’s ratios are numerically optimized and then fabricated using selective laser sintering. Practical Poisson's ratios of the samples are evaluated by conducting simulation and compression experiments. The tested Poisson's ratios by the compression experiment match the numerical estimation of the proposed method in a high consistency, which demonstrates the advances of our design method for creating reliable auxetic microstructures for 3D printing. The failure test is also implemented on different microstructures. It is concluded that the devised chiral metamaterial exhibits a great ability to absorb external deformation energy.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig.14
Fig.15
Fig. 16
Fig. 17
Fig. 18
Fig. 19

Similar content being viewed by others

Data availability

The authors confirm that the data supporting the findings of this study are available within the article.

References

  1. Askari M, Hutchins DA, Thomas PJ, Astolfi L, Watson RL, Abdi M, Ricci M, Laureti S, Nie L, Freear S, Wildman R, Tuck C, Clarke M, Woods E, Clare AT (2020) Additive manufacturing of metamaterials: a review. Addit Manuf 36:101562

    Google Scholar 

  2. Lee JH, Singer JP, Thomas EL (2012) Micro-/nanostructured mechanical metamaterials. Adv Mater 24:4782–4810

    Google Scholar 

  3. Lakes R (1987) Foam structures with a negative Poisson’s ratio. Science 235:1038–1041

    Google Scholar 

  4. Huang C, Chen L (2016) Negative Poisson’s ratio in modern functional materials. Adv Mater 28:8079–8096

    Google Scholar 

  5. Liu W, Wang N, Luo T, Lin Z (2016) In-plane dynamic crushing of re-entrant auxetic cellular structure. Mater Des 100:84–91

    Google Scholar 

  6. Fu MH, Zheng BB, Li WH (2017) A novel chiral three-dimensional material with negative Poisson’s ratio and the equivalent elastic parameters. Compos Struct 176:442–448

    Google Scholar 

  7. Fu M, Liu F, Hu L (2018) A novel category of 3D chiral material with negative Poisson’s ratio. Compos Sci Technol 160:111–118

    Google Scholar 

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

    MathSciNet  Google Scholar 

  9. Bendsøe MP, Sigmund O (2003) Topology Optimization: Theory, Methods, and Applications. Springer, Berlin, Heidelberg

    Google Scholar 

  10. Bendsøe MP, Kikuchi N (1988) Generating optimal topologies in structural design using a homogenization method. Comput Methods Appl Mech Eng 71:197–224

    MathSciNet  Google Scholar 

  11. Zhou M, Rozvany GIN (1991) The COC algorithm, part II: topological, geometry and generalized shape optimization. Comput Methods Appl Mech Eng 89:309–336

    Google Scholar 

  12. Bendsøe MP, Sigmund O (1999) Material interpolation schemes in topology optimization. Arch Appl Mech 69:635–654

    Google Scholar 

  13. Sigmund O (2001) A 99 line topology optimization code written in Matlab. Struct Multidiscip Optim 21:120–127

    Google Scholar 

  14. Xie YM, Steven GP (1993) A simple evolutionary procedure for structural optimization. Comput Struct 49:885–896

    Google Scholar 

  15. Osher S, Sethian JA (1988) Fronts propagating with curvature-dependent speed-algorithms based on Hamilton-Jacobi formulations. J Comput Phys 79:12–49

    MathSciNet  Google Scholar 

  16. Sethian JA, Wiegmann A (2000) Structural boundary design via level set and immersed interface methods. J Comput Phys 163:489–528

    MathSciNet  Google Scholar 

  17. Wang MY, Wang XM, Guo DM (2003) A level set method for structural topology optimization. Comput Methods Appl Mech Eng 192:227–246

    MathSciNet  Google Scholar 

  18. Allaire G, Jouve F, Toader AM (2004) Structural optimization using sensitivity analysis and a level-set method. J Comput Phys 194:363–393

    MathSciNet  Google Scholar 

  19. Guo X, Zhang W, Zhong W (2014) Doing topology optimization explicitly and geometrically—a new moving morphable components based framework. J Appl Mech 81:081009

    Google Scholar 

  20. Norato JA, Bell BK, Tortorelli DA (2015) A geometry projection method for continuum-based topology optimization with discrete elements. Comput Methods Appl Mech Eng 293:306–327

    MathSciNet  Google Scholar 

  21. Zhou Y, Zhang W, Zhu J, Xu Z (2016) Feature-driven topology optimization method with signed distance function. Comput Methods Appl Mech Eng 310:1–32

    MathSciNet  Google Scholar 

  22. Sigmund O (1994) Materials with prescribed constitutive parameters: An inverse homogenization problem. Int J Solids Struct 31:2313–2329

    MathSciNet  Google Scholar 

  23. Radman A, Huang X, Xie YM (2012) Topology optimization of functionally graded cellular materials. J Mater Sci 48:1503–1510

    Google Scholar 

  24. Xu B, Jiang JS, Xie YM (2015) Concurrent design of composite macrostructure and multi-phase material microstructure for minimum dynamic compliance. Compos Struct 128:221–233

    Google Scholar 

  25. Long K, Du X, Xu S, Xie YM (2016) Maximizing the effective Young’s modulus of a composite material by exploiting the poisson effect. Compos Struct 153:593–600

    Google Scholar 

  26. Liu Q, Chan R, Huang X (2016) Concurrent topology optimization of macrostructures and material microstructures for natural frequency. Mater Des 106:380–390

    Google Scholar 

  27. Dong H-W, Wang Y-S, Zhang C (2017) Topology optimization of chiral phoxonic crystals with simultaneously large phononic and photonic bandgaps. IEEE Photonics J 9:1–16

    Google Scholar 

  28. Duan S, Xi L, Wen W, Fang D (2020) Mechanical performance of topology-optimized 3D lattice materials manufactured via selective laser sintering. Compos Struct 238:111985

    Google Scholar 

  29. Das S, Sutradhar A (2020) Multi-physics topology optimization of functionally graded controllable porous structures: application to heat dissipating problems. Mater Des 193:108775

    Google Scholar 

  30. Zhang X, Ye H, Wei N, Tao R, Luo Z (2021) Design optimization of multifunctional metamaterials with tunable thermal expansion and phononic bandgap. Mater Des 209:109990

    Google Scholar 

  31. Zhang H, Takezawa A, Ding X, Xu S, Duan P, Li H, Guo H (2021) Bi-material microstructural design of biodegradable composites using topology optimization. Mater Des 209:109973

    Google Scholar 

  32. Zhou Y, Gao L, Li H (2022) Graded infill design within free-form surfaces by conformal mapping. Int J Mech Sci 224:107307

    Google Scholar 

  33. Wang Y, Luo Z, Zhang N, Kang Z (2014) Topological shape optimization of microstructural metamaterials using a level set method. Comput Mater Sci 87:178–186

    Google Scholar 

  34. Clausen A, Wang F, Jensen JS, Sigmund O, Lewis JA (2015) Topology optimized architectures with programmable poisson’s ratio over large deformations. Adv Mater 27:5523–5527

    Google Scholar 

  35. Zhang H, Luo Y, Kang Z (2018) Bi-material microstructural design of chiral auxetic metamaterials using topology optimization. Compos Struct 195:232–248

    Google Scholar 

  36. Schwerdtfeger J, Wein F, Leugering G, Singer RF, Korner C, Stingl M, Schury F (2011) Design of auxetic structures via mathematical optimization. Adv Mater 23:2650–2654

    Google Scholar 

  37. Andreassen E, Lazarov BS, Sigmund O (2014) Design of manufacturable 3D extremal elastic microstructure. Mech Mater 69:1–10

    Google Scholar 

  38. Wang F (2018) Systematic design of 3D auxetic lattice materials with programmable Poisson’s ratio for finite strains. J Mech Phys Solids 114:303–318

    MathSciNet  Google Scholar 

  39. Li Z, Gao W, Yu Wang M, Luo Z (2022) Design of multi-material isotropic auxetic microlattices with zero thermal expansion. Mater Des 222:111051

    Google Scholar 

  40. Vogiatzis P, Chen S, Wang X, Li T, Wang L (2017) Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method. Comput Aided Des 83:15–32

    MathSciNet  Google Scholar 

  41. Zong H, Zhang H, Wang Y, Wang MY, Fuh JYH (2018) On two-step design of microstructure with desired Poisson’s ratio for AM. Mater Des 159:90–102

    Google Scholar 

  42. van Dijk NP, Maute K, Langelaar M, van Keulen F (2013) Level-set methods for structural topology optimization: a review. Struct Multidiscip Optim 48:437–472

    MathSciNet  Google Scholar 

  43. Svanberg K (1987) The method of moving asymptotes-a new method for structural optimization. Inter J Numerical Methods Eng 24:359–373

    MathSciNet  Google Scholar 

  44. Luo Z, Tong L, Kang Z (2009) A level set method for structural shape and topology optimization using radial basis functions. Comput Struct 87:425–434

    Google Scholar 

  45. Buhmann MD (2004) Radial Basis Functions: Theory and Implementations, Cambridge Monographs on Applied and Computational Mathematics, vol 12. Cambridge University Press, New York

    Google Scholar 

  46. H. Wendland, Computational aspects of radial basis function approximation, Elsevier BV, 2005.

  47. Chen K (1999) Discrete wavelet transforms accelerated sparse preconditioners for dense boundary element systems. Electron Trans Numer Anal 8:138–153

    MathSciNet  Google Scholar 

  48. Ravnik J, Škerget L, Hriberšek M (2004) The wavelet transform for BEM computational fluid dynamics. Eng Anal Boundary Elem 28:1303–1314

    Google Scholar 

  49. Beylkin G, Coifman R, Rokhlin V (1991) Fast wavelet transforms and numerical algorithms. Communications Pure And Applied Mathematics 44:141–183

    MathSciNet  Google Scholar 

  50. Guedes JM, Kikuchi N (1990) Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods. Comput Methods Appl Mech Eng 83:143–198

    MathSciNet  Google Scholar 

  51. Chen L, Li X (2018) An Interpolating boundary element-free method for 2D helmholtz equations. Appl Math Mech 39:470–484

    Google Scholar 

  52. Zhou Y, Li H, Li X, Gao L (2022) Design of multiphase auxetic metamaterials by a parametric color level set method. Compos Struct 287:115385

    Google Scholar 

  53. Andreassen E, Andreasen CS (2014) How to determine composite material properties using numerical homogenization. Comput Mater Sci 83:488–495

    Google Scholar 

  54. Wang X, Mei Y, Wang MY (2005) Level-set method for design of multi-phase elastic and thermoelastic materials. Int J Mech Mater Des 1:213–239

    Google Scholar 

  55. Holt JM, Ho CY (1996) CINDAS. Purdue University, West Lafayette, Structural Alloy Handbook

    Google Scholar 

  56. U.S. Department of Transportation, Metallic Materials Properties Development and Standardization (MMPDS), in, Knovel Library, 2003.

Download references

Acknowledgements

This research is partially supported by the National Natural Science Foundation of China (52075195), and the Fundamental Research Funds for the Central Universities (2172019kfyXJJS078).

Author information

Authors and Affiliations

  1. State Key Lab of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, 1037 Luoyu Road, Wuhan, 430074, Hubei, China

    Ying Zhou, Liang Gao & Hao Li

Authors
  1. Ying Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Hao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hao Li.

Ethics declarations

Conflict of interest

The authors have no competing interests to declare that are relevant to the content of this article.

Additional information

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, Y., Gao, L. & Li, H. A ready-to-manufacture optimization design of 3D chiral auxetics for additive manufacturing. Engineering with Computers 40, 1517–1538 (2024). https://doi.org/10.1007/s00366-023-01880-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-023-01880-1

Keywords

Search

Navigation