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Modeling of uniaxial compression in a 3D periodic re-entrant lattice structure

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Abstract

In this study, the behavior of a parametric 3D re-entrant dodecahedron lattice structure with negative Poisson’s ratio was studied. Four geometrical configurations for the re-entrant dodecahedron were designed, and the relationship between the mechanical properties and the design parameters was determined through beam theory. Samples were fabricated successfully via electron beam melting. Compressive tests as well as finite element analysis (FEA) were performed, and the results were compared with theoretical predictions. The modeling yielded explicit analytical equations of various mechanical properties including Poisson’s ratios, modulus and strength, and the compressive strength and the modulus from the prediction match well with the experiments, as well as the FEA results. The methodology used by this study also demonstrated a feasible approach to design 3D auxetic cellular structure for various applications.

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  • 26 April 2020

    In the original article, there is a typographical error in the in-line equation on page 1418 following Eq. (21). The sentence should read as follows.

References

  1. Lakes R (1987) Science 235:1038

    Article  CAS  Google Scholar 

  2. Scarpa F, Tomlin PJ (2000) Fatigue Fract Eng Mater Struct 23:717

    Article  CAS  Google Scholar 

  3. Lakes RS (1993) J Mech Des 115:696

    Article  Google Scholar 

  4. Scarpa F, Tomlinson G (2000) J Sound Vib 230:45

    Article  Google Scholar 

  5. Lakes RS, Elms K (1993) J Compos Mater 27:1193

    Article  Google Scholar 

  6. Alderson KL, Simkins VR, Coenen VL, Davies PJ, Alderson A, Evans KE (2009) Phys Status Solidi B 57:1865

    Google Scholar 

  7. Bianchi M, Scarpa FL, Smith CW (2008) J Mater Sci 43:5851. doi:10.1007/s10853-008-2841-5

    Article  CAS  Google Scholar 

  8. Bezazi A, Scarpa F (2007) Int J Fatigue 29:922

    Article  CAS  Google Scholar 

  9. Bezazi A, Scarpa F (2009) Int J Fatigue 31:488

    Article  CAS  Google Scholar 

  10. Scarpa F, Pastorino P, Garelli A, Patsias S, Ruzzene M (2005) Phys Status Solidi B 242:681

    Article  CAS  Google Scholar 

  11. Scarpa F, Ciffo LG, Yates JR (2004) Smart Mater Struct 13:49

    Article  CAS  Google Scholar 

  12. Howell B, Prendergast P, Hansen L (1996) Appl Acoust 43:141

    Article  Google Scholar 

  13. Scarpa F, Smith FC (2004) J Intell Mater Syst Struct 15:973

    Article  CAS  Google Scholar 

  14. Scarpa F, Bullough WA, Lumley P (2004) Proc Inst Mech Eng Part C 218:241

    Article  CAS  Google Scholar 

  15. Almgren RF (1985) J Elast 15:427

    Article  Google Scholar 

  16. Prall D, Lakes RS (1996) Int J Mech Sci 39:305

    Article  Google Scholar 

  17. Grima JN (2006) J Mater Sci 41:3193. doi:10.1007/s10853-006-6339-8

    Article  CAS  Google Scholar 

  18. Gaspar N, Smith CW, Alderson A, Grima JN, Evans KE (2011) J Mater Sci 46:372. doi:10.1007/s10853-010-4846-0

    Article  CAS  Google Scholar 

  19. Grima JN, Ravirala N, Galea R, Ellul B, Attard D, Gatt R, Alderson A, Rasburn J, Evans KE (2011) Phys Status Solidi B 248:117

    Article  CAS  Google Scholar 

  20. Williams JJ, Smith CW, Evans KE, Lethbridge ZAD, Walton RI (2007) Acta Mater 55:5697

    Article  CAS  Google Scholar 

  21. Caddock BD, Evans KE (1989) J Phys D Appl Phys 22:1877

    Article  CAS  Google Scholar 

  22. Theocaris PS, Stavroulakis GE, Panagiotopoulos PD (1997) Arch Appl Mech 67:274

    Article  Google Scholar 

  23. Larsen UD, Sigmund O, Bouwstra S (1997) Int J Mech Sci 6:99

    Google Scholar 

  24. Evans KE, Caddock BD (1989) J Phys D Appl Phys 22:1883

    Article  CAS  Google Scholar 

  25. Wan H, Ohtaki H, Kotosaka S, Hu G (2004) Eur J Mech A/Solids 23:95

    Article  Google Scholar 

  26. Evans KE, Nkansah MA, Hutchinson IJ (1994) Acta Metall et Mater 42:1289

    Article  Google Scholar 

  27. Schwerdtfeger J, Heinl P, Singer RF, Korner C (2010) Phys Status Solidi B 247:269

    Article  CAS  Google Scholar 

  28. Lakes RS, Witt R (2002) Int J Mech Eng Educ 30:50

    Google Scholar 

  29. Brezny R, Green DJ (1990) J Mater Sci 25:4571. doi:10.1007/BF01129908

    Article  CAS  Google Scholar 

  30. Gibson LJ, Ashby MF (1997) Cellular solids: structure and properties, 2nd edn. Cambridge University Press, Cambridge

    Google Scholar 

  31. Onck PR, Andrews EW, Gibson LJ (2001) Int J Mech Sci 43:681

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Edward P. Fitts Department of Industrial & System Engineering, North Carolina State University, 400 Daniels Hall, 111 Lampe Dr., Raleigh, NC, 27695, USA

    Li Yang, Ola Harrysson & Harvey West

  2. Department of Industrial & System Engineering, Rochester Institute of Technology, James E. Gleanson Building, 81 Lomb Memorial Dr., Rochester, NY, 14623, USA

    Denis Cormier

Authors
  1. Li Yang
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  2. Ola Harrysson
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  3. Harvey West
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  4. Denis Cormier
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Correspondence to Ola Harrysson.

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Yang, L., Harrysson, O., West, H. et al. Modeling of uniaxial compression in a 3D periodic re-entrant lattice structure. J Mater Sci 48, 1413–1422 (2013). https://doi.org/10.1007/s10853-012-6892-2

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  • DOI: https://doi.org/10.1007/s10853-012-6892-2

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