Skip to main content
SpringerLink
Log in

Linear Homogenization in the Analysis of Cellular Structures Produced by Additive Technology

  • Published:
Russian Engineering Research Aims and scope

Abstract

Linear homogenization is applied to cellular structures produced by selective laser melting (SLM). Samples of different materials with cells of different configurations are studied theoretically and experimentally. Their strain curves are compared with the results for bulk and beam models and with experimental data. After homogenization, the rigidity of the homogenized model differs by 5–10% from the beam model and by 8–16% from the bulk model.

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

Access this article

Log in via an institution

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.

Similar content being viewed by others

REFERENCES

  1. Gibson, I., Rosen, D., and Stucker, B., Additive Manufacturing Technologies: 3D Printing, Rapid Prototyping, and Direct Digital Manufacturing, New York: Springer, 2015.

    Book  Google Scholar 

  2. Kablov, E.N., Additive technologies as a keystone of the national technology initiative, Intell. Tekhnol., 2015, no. 2 (11), pp. 52–55.

  3. Kablov, E.N., Innovative developments of the All-Russian Scientific Research Institute of Aviation Materials within the project “Strategic development of materials and technologies of their recycling until 2030,” Aviats. Mater. Tekhnol., 2015, no. 1 (34), pp. 3–33. https://doi.org/10.18577/2071-9140-2015-0-1-3-33

  4. Kablov, E.N., Development of Russian national material science for space, Vestn. RFFI, 2017, no. 3, pp. 97–105.

  5. Vostrikov, A.V. and Sukhov, D.I., Production of pellets for additive technologies by PREP method: current status and prospective development, Tr. Vseross. Nauchno-Issled. Inst. Aviats. Mater., 2016, no. 8, art. 3. http://www.viam-works.ru. Accessed June 15, 2019.https://doi.org/10.18577/2307-6046-2016-0-8-3-3

  6. Kablov, E.N., The materials as a key problem, in Tendentsii i orientiry innovatsionnogo razvitiya Rossii (Trends and Benchmarks of Innovative Development in Russia), Moscow: Vseross. Nauchno-Issled. Inst. Aviats. Mater., 2015, pp. 458–464.

  7. Gibson, L.J. and Ashby, M.F., Cellular Solids: Structure and Properties, Cambridge: Cambridge Univ. Press, 1999.

    MATH  Google Scholar 

  8. Sukhov, D.I., Mazalov, P.B., Nerush, S.V., and Khodyrev, N.A., Influence of the parameters of selective laser sintering on the porosity degree in the synthesized material of corrosion-resistant steel, Tr. Vseross. Nauchno-Issled. Inst. Aviats. Mater., 2017, no. 8 (56), art. 4. http://www.viam-works.ru. Accessed June 15, 2019.https://doi.org/10.18577/2307-6046-2017-0-8-4-4

  9. Rehme, O. and Emmelmann, C., Rapid manufacturing of lattice structures with selective laser melting, Proc. SPIE, 2006, vol. 6107, pp. 61070K-1–61070K-12. https://doi.org/10.1117/12.645848

    Article  Google Scholar 

  10. Hill, R., Elastic properties of reinforced solids: some theoretical principles, J. Mech. Phys. Solids, 1963, vol. 11, no. 5, pp. 357–372. https://doi.org/10.1016/0022-5096(63)90036-x

    Article  MATH  Google Scholar 

  11. Huet, C., Application of variational concepts to size effects in elastic heterogeneous bodies, J. Mech. Phys. Solids, 1990, vol. 38, pp. 813–841. https://doi.org/10.1016/0022-5096(90)90041-2

    Article  MathSciNet  Google Scholar 

  12. Sab, K. On the homogenization and the simulation of random materials, Eur. J. Mech., 1992, vol. 11, pp. 585–607.

    MathSciNet  MATH  Google Scholar 

  13. Sun, C.T. and Vaidya, R.S., Prediction of composite properties from a representative volume element, Compos. Sci. Technol., 1996, vol. 56, pp. 171–179. https://doi.org/10.1016/0266-3538(95)00141-7

    Article  Google Scholar 

  14. Christensen, R.M., Mechanics of Composite Materials, Chichester: Wiley, 1979.

    Google Scholar 

  15. Nasedkin, A.V. and Shevtsova, M.S., Effective moduli simulation for various types of porous piezoceramic materials, Vestn. Donsk. Gos. Tekh. Univ., 2013, nos. 3–4, pp. 72–73.

  16. Annin, B.D. and Ostrosablin, N.I., Anisotropy of elastic properties of materials, J. Appl. Mech. Tech. Phys., 2008, vol. 49, no. 6, pp. 998–1014.

    Article  MathSciNet  Google Scholar 

  17. Ivanov, M.L., Analysis and modeling of the mechanical behavior of brickwork as an elastic-brittle system, Trudy Mezhdunarodnoi mauchnoi konferentsii “Tekhnicheskie nauki: problemy i perspektivy” (Proc. Int. Sci. Conf. “Technical Sciences: Problems and Prospects”), St. Petersburg: Renome, 2011, pp. 58–62. https://moluch.ru/conf/tech/archive/2/146/. Accessed June 15, 2019.

  18. Evgenov, A.G., Gorbovets, M.A., and Prager, S.M., Structure and mechanical properties of VZh159 and EP648 heat-resistant alloys obtained by selective laser sintering, Aviats. Mater. Tekhnol., 2016, suppl. 1, pp. 8–15. https://doi.org/10.18577/2071-9140-2016-0-S1-8-15

  19. Yakovlev, N.O., Grinevich, D.V., and Mazalov, P.B., Mathematical modeling of the stress-strain state of compressed mesh construction synthesized by selective laser sintering, Vestn. MGTU N. E. Baumana, Ser. Estestv. Nauki, 2018, no. 6 (81), pp. 113–127. https://doi.org/10.18698/1812-3368-2018-6-113-127

Download references

Author information

Authors and Affiliations

  1. Russian Institute of Aviation Materials, Moscow, Russia

    D. V. Grinevich, N. O. Yakovlev & P. B. Mazalov

Authors
  1. D. V. Grinevich
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. O. Yakovlev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. B. Mazalov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. V. Grinevich.

Additional information

Translated by B. Gilbert

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Grinevich, D.V., Yakovlev, N.O. & Mazalov, P.B. Linear Homogenization in the Analysis of Cellular Structures Produced by Additive Technology. Russ. Engin. Res. 41, 423–427 (2021). https://doi.org/10.3103/S1068798X2105004X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S1068798X2105004X

Keywords:

Search

Navigation