Coupling finite element method with large scale atomic/molecular massively parallel simulator (LAMMPS) for hierarchical multiscale simulations

Modeling and simulation of amorphous polymeric materials

Abstract

In this work, we have developed a multiscale computational algorithm to couple finite element method with an open source molecular dynamics code – the large scale atomic/molecular massively parallel simulator (LAMMPS) – to perform hierarchical multiscale simulations in highly scalable parallel computations. The algorithm was firstly verified by performing simulations of single crystal copper deformation, and a good agreement with the well-established method was confirmed. Then, we applied the multiscale method to simulate mechanical responses of a polymeric material composed of multi-million fine scale atoms inside the representative unit cells (r-cell) against uniaxial loading. It was observed that the method can successfully capture plastic deformation in the polymer at macroscale, and reproduces the double yield points typical in polymeric materials, strain localization and necking deformation after the second yield point. In addition, parallel scalability of the multiscale algorithm was examined up to around 100 thousand processors with 10 million particles, and an almost ideal strong scaling was achieved thanks to LAMMPS parallel architecture.

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References

  1. 1.

    E.B. Tadmor, R.E. Miller,Modeling materials: continuum, atomistic and multiscale techniques (Cambridge University Press, Cambridge, 2011)

  2. 2.

    W.K. Liu, E.G. Karpov, S. Zhang, H.S. Park, Comput. Methods Appl. Mech. Eng. 193, 1529 (2004)

    ADS  Article  Google Scholar 

  3. 3.

    A.C. To, S. Li, Phys. Rev. B 72, 035414 (2005)

    ADS  Article  Google Scholar 

  4. 4.

    T. Murashima, S. Yasuda, T. Taniguchi, R. Yamamoto, J. Phys. Soc. Jpn. 82, 012001 (2013)

    ADS  Article  Google Scholar 

  5. 5.

    F.F. Abraham, J.Q. Broughton, N. Bernstein, E. Kaxiras, Europhys. Lett. 44, 783 (1998)

    ADS  Article  Google Scholar 

  6. 6.

    J.Q. Broughton, F.F. Abraham, N. Bernstein, E. Kaxiras, Phys. Rev. B 60, 2391 (1999)

    ADS  Article  Google Scholar 

  7. 7.

    G.J. Wagner, W.K. Liu, J. Comput. Phys. 190, 249 (2003)

    ADS  Article  Google Scholar 

  8. 8.

    S.P. Xiao, T. Belytschko, Comput. Methods Appl. Mech. Eng. 193, 1645 (2004)

    ADS  Article  Google Scholar 

  9. 9.

    S. Li, S. Urata, Comput. Methods Appl. Mech. Eng. 306, 452 (2016)

    ADS  Article  Google Scholar 

  10. 10.

    S. Urata, S. Li, A multiscale molecular dynamics and coupling with nonlinear finite element method, inWorkshop on Coupled Mathematical Models for Physical and Nanoscale Systems and their Applications (Springer, Berlin, 2016), pp. 215–244

  11. 11.

    Q. Tong, S. Li, J. Mech. Phys. Solids 95, 169 (2016)

    ADS  MathSciNet  Article  Google Scholar 

  12. 12.

    N. Sheng, M.C. Boyce, D.M. Parks, G.C. Rutledge, J.I. Abes, R.E. Cohen, Polymer 45, 487 (2004)

    Article  Google Scholar 

  13. 13.

    P.K. Valavala, T.C. Clancy, G.M. Odegard, T.S. Gates, E.C. Aifantis, Acta Mater. 57, 525 (2009)

    Article  Google Scholar 

  14. 14.

    J.M. Wernik, S.A. Meguid, Int. J. Solids Struct. 51, 2575 (2014)

    Article  Google Scholar 

  15. 15.

    E.B. Tadmor, M. Ortiz, R. Phillips, Philos. Mag. A 73, 1529 (1996)

    ADS  Article  Google Scholar 

  16. 16.

    E.B. Tadmor, G.S. Smith, N. Bernstein, E. Kaxiras, Phys. Rev. B 59, 235 (1999)

    ADS  Article  Google Scholar 

  17. 17.

    R.E. Miller, E.B. Tadmor, J. Computer-Aided Mater. Des. 9, 203 (2002)

    ADS  Article  Google Scholar 

  18. 18.

    R. Sunyk, P. Steinmann, Int. J. Solids Struct. 40, 6877 (2003)

    Article  Google Scholar 

  19. 19.

    E. Weinan, P. Ming, Arch. Ration. Mech. Anal. 183, 241 (2007)

    MathSciNet  Article  Google Scholar 

  20. 20.

    D. Lyu, S. Li, J. Mech. Phys. Solids 107, 379 (2017)

    ADS  MathSciNet  Article  Google Scholar 

  21. 21.

    D. Lyu, S. Li, J. Mech. Phys. Solids 122, 613 (2019)

    ADS  MathSciNet  Article  Google Scholar 

  22. 22.

    S. Urata, S. Li, Int. J. Fract. 203, 159 (2017)

    Article  Google Scholar 

  23. 23.

    S. Urata, S. Li, Acta Mater. 155, 153 (2018)

    Article  Google Scholar 

  24. 24.

    M. Parrinello, A. Rahman, Phys. Rev. Lett. 45, 1196 (1980)

    ADS  Article  Google Scholar 

  25. 25.

    S. Urata, S. Li, Comput. Mater. Sci. 135, 64 (2017)

    Article  Google Scholar 

  26. 26.

    S. Plimpton, J. Comput. Phys. 117, 1 (1995)

    ADS  Article  Google Scholar 

  27. 27.

    LAMMPS, https://lammps.sandia.gov/

  28. 28.

    Y. Mishin, M.J. Mehl, D.A. Papaconstantopoulos, A.F. Voter, J.D. Kress, Phys. Rev. B 63, 224106 (2001)

    ADS  Article  Google Scholar 

  29. 29.

    K. Kremer, G.S. Grest, J. Chem. Phys. 92, 5057 (1990)

    ADS  Article  Google Scholar 

  30. 30.

    OCTA, http://octa.jp

  31. 31.

    T. Murashima, K. Hagita, T. Kawakatsu, J. Soc. Rheol. Jpn. (Nihon Reoroji Gakkaishi) 46, 207 (2018)

    Article  Google Scholar 

  32. 32.

    C. Bennenmann, W. Paul, K. Binder, B. Dunweg, Phys. Rev. E 57, 843 (1998)

    ADS  Article  Google Scholar 

  33. 33.

    N.W. Brooks, R.A. Duckett, I.M. Ward, Polymer 33, 1872 (1992)

    Article  Google Scholar 

  34. 34.

    K. Yashiro, T. Ito, Y. Tomita, Int. J. Mech. Sci. 45, 1863 (2003)

    Article  Google Scholar 

  35. 35.

    Y. Higuchi, M. Kubo, Macromolecules 50, 3690 (2017)

    ADS  Article  Google Scholar 

  36. 36.

    H.Y. Zhou, G.L. Wilkes, J. Mater. Sci. 33, 287 (1998)

    ADS  Article  Google Scholar 

  37. 37.

    What is K? https://www.r-ccs.riken.jp/en/k-computer/

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Authors

Contributions

TM designed the concurrent coupling algorithm and developed a code to establish interface with LAMMPS. SU developed the multiscale simulation code coupling FEM and LAMMPS, and performed validation tests. TM conducted large scale simulation for the polymeric material. TM and SU wrote simulation parts of the manuscript, and SL supervised the project, wrote and summarized the manuscript. All the authors have read and approved the final manuscript.

Corresponding author

Correspondence to Takahiro Murashima.

Additional information

Contribution to the Topical Issue “Multiscale Materials Modeling”, edited by Yoji Shibutani, Shigenobu Ogata, and Tomotsugu Shimokawa.

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Murashima, T., Urata, S. & Li, S. Coupling finite element method with large scale atomic/molecular massively parallel simulator (LAMMPS) for hierarchical multiscale simulations. Eur. Phys. J. B 92, 211 (2019). https://doi.org/10.1140/epjb/e2019-100105-9

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