Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Numerical simulation of selective laser melting with local powder shrinkage using FEM with the refined mesh


A mathematical model of selective laser melting (SLM) of fine-grained metallic powders under the pulse laser annealing conditions has been developed. The processed powder bed is considered in the approximation of continuous medium where its effective thermophysical properties depend on local porosity. The model allows simulation of unsteady distributions of temperature, specific enthalpy, local porosity, morphology and thickness of the processed track. In the paper, all stages of problem analysis are described including its mathematical formulation and numerical implementation. To take into account shrinkage of the powder layer during sintering and remelting, the numerical model utilizes the arbitrary Lagrangian–Eulerian (ALE) method. Thus the finite element mesh provides robust control of quality and dynamic remeshing through adaptive mesh refinement. Using the proposed numerical model the unsteady thermal fields and local porosity of a Fe-based powder layer processed with a pulsed laser has been investigated.

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


  1. 1.

    E.V. Haranzhevskiy, D.A. Danilov, M.D. Krivilyov, P.K. Galenko, Mater. Sci. Eng. A 375–377, 502 (2004)

  2. 2.

    S. Kumar, JOM 55, 43 (2003)

  3. 3.

    I.V. Shishkovskiy, in Fundamentals of additive technologies of high resolution (SpB, Saint-Petersburg, 2016), p. 400

  4. 4.

    E.V. Kharanzhevskiy, M.D. Krivilyov, Phys. Met. Metall. 111, 53 (2011)

  5. 5.

    W.E. King, A.T. Anderson, R.M. Ferencz, N.E. Hodge, C. Kamath, S.A. Khairallah, A.M. Rubenchik, Appl. Phys. Rev. 2, 41304 (2015)

  6. 6.

    V. Viswanathan, T. Laha, K. Balani, A. Agarwal, S. Seal, Mater. Sci. Eng. R 54, 121 (2006)

  7. 7.

    D.M. Herlach, Mater. Sci. Eng. R 12, 177 (1994)

  8. 8.

    C. Meier, R.W. Penny, Y. Zou, J.S. Gibbs, A.J. Hart, Annu. Rev. Heat Transfer 20 (2017).

  9. 9.

    C.Y. Yap, C.K. Chua, Z.L. Dong, Z.H. Liu, D.Q. Zhang, L.E. Loh, S.L. Sing, Appl. Phys. Rev. 2, 41101 (2015)

  10. 10.

    S.A. Khairallah, A.T. Anderson, A. Rubenchik, W.E. King, Acta Mater. 108, 36 (2016)

  11. 11.

    A.G. Knyazeva, S.A. Shanin, Acta Mech. 227, 75 (2016)

  12. 12.

    Q. Chen, G. Guillemot, C.A. Gandin, M. Bellet, Addit. Manuf. 21, 713 (2018)

  13. 13.

    J.D. Williams, C.R. Deckard, Rapid Prototyp. J. 4, 90 (1998)

  14. 14.

    N.E. Hodge, R.M. Ferencz, J.M. Solberg, Comput. Mech. 54, 33 (2014)

  15. 15.

    M. Jamshidinia, F. Kong, R. Kovacevic, ASME District F-ECTC 1, 1 (2013)

  16. 16.

    T.S. Volchenko, A.P. Yalovets, Tech. Phys. 61, 324 (2016)

  17. 17.

    M.D. Krivilev, D.D. Aflyatunova, V. Ankudinov, G.A. Gordeev, Materialovedenie (Mater. Sci.) 1, 2 (2012)

  18. 18.

    I.V. Shutov, G.A. Gordeev, E.V. Kharanzhevskiy, M.D. Krivilyov, I.O.P. Conf, Ser, Mater. Sci. Eng. 192, 12023 (2017)

  19. 19.

    V. Ankudinov, G.A. Gordeev, M.D. Krivilyov, I.O.P. Conf, Ser, Mater. Sci. Eng. 192, 12026 (2017)

  20. 20.

    M.D. Krivilyov, S.D. Mesarovic, D.P. Sekulic, J. Mater. Sci. 0022–2461, 1 (2016)

  21. 21.

    G.A. Gordeev, M.D. Krivilyov, V. Ankudinov, Comput. Continuum Mech. 10, 293 (2017)

  22. 22.

    B.R. Bird, E.S. Warren, N.E. Lightfoot, in Transport Phenomena (John Wiley & Sons, 2007), p. 905

  23. 23.

    I. Gibson, D. Rosen, B. Stuker, in Additive manufacturing technologies: 3D printing, rapid Prototyping, and direct digital manufacturing (2013), p. 10

  24. 24.

    M.D. Krivilyov, G.A. Gordeev, V. Ankudinov, I.V. Shutov, E.V., Kharanzhevskiy, Additive technologies: now and future, in Proceedings of 4th International conference (VIAM, 2018), Vol. 1, pp. 1–15

  25. 25.

    L.J. Segerlind, in Applied finite element analysis (Wiley, 1984), p. 448

  26. 26.

    O. Zienkiewicz, R.L. Taylor, in Finite element method in engineering science (McGraw-Hill, 2000), p. 521

  27. 27.

    J. Donea, A. Huerta, J.P. Ponthot, A. Rodríguez-Ferran, Fundamentals, in Encyclopedia of computational mechanics (John Wiley & Sons, 2004), Vol. 1, pp. 1–25

  28. 28.

    COMSOL Multiphysics User Guide, COMSOL AB, 2012

Download references

Author information

Correspondence to Georgiy A. Gordeev.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gordeev, G.A., Ankudinov, V., Kharanzhevskiy, E.V. et al. Numerical simulation of selective laser melting with local powder shrinkage using FEM with the refined mesh. Eur. Phys. J. Spec. Top. 229, 205–216 (2020).

Download citation