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Study of the shear-band evolution across the interface between different spatial scales

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Abstract

Much research has been performed for multiscale modeling and simulation of physical phenomena, but it is still a challenging task to effectively describe the evolution of failure across the interface between different spatial scales. Although molecular dynamics (MD) at nanoscale, smoothed molecular dynamics (SMD) at mesoscale and material point method (MPM) at micro- and macro-scales have been combined for multiscale simulations of different problems such as uniaxial tension, bending and plate ones, how to simulate the evolution of shear band across different scales remains to be an open issue. As a result, there is a lack of knowledge in objectively evaluating multiscale failure evolution in general. An effort is therefore made in this work to investigate how the shear banding could evolve between different scales with integrated MD and SMD in a single computational domain, which is verified via a convergence study. The interfacial effect on failure evolution is then explored for the future concurrent MD/SMD/MPM simulations of different physical phenomena under extreme loading conditions.

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References

  1. He N, Liu Y, Zhang X (2015) An improved smoothed molecular dynamics method by alternating with molecular dynamics. Comput Methods Appl Mech Eng 296:273–294. https://doi.org/10.1016/j.cma.2015.08.005

    Article  ADS  MathSciNet  Google Scholar 

  2. He N, Liu Y, Zhang X (2016) Molecular dynamics-smoothed molecular dynamics (MD-SMD) adaptive coupling method with seamless transition. Int J Numer Meth Eng 108(3):233–251

    Article  MathSciNet  Google Scholar 

  3. He N, Liu Y, Zhang X (2017) Seamless coupling of molecular dynamics and material point method via smoothed molecular dynamics. Int J Numer Meth Eng 112(4):380–400. https://doi.org/10.1002/nme.5543

    Article  MathSciNet  Google Scholar 

  4. Chen Z, Jiang S, Gan Y, Liu H, Sewell TD (2014) A particle-based multiscale simulation procedure within the material point method framework. Comput Part Mech 1(2):147–158. https://doi.org/10.1007/s40571-014-0016-5

    Article  Google Scholar 

  5. Jiang S, Chen Z, Sewell TD, Gan Y (2015) Multiscale simulation of the responses of discrete nanostructures to extreme loading conditions based on the material point method. Comput Methods Appl Mech Eng 297:219–238. https://doi.org/10.1016/j.cma.2015.08.009

    Article  ADS  MathSciNet  Google Scholar 

  6. Liu B, Huang Y, Jiang H, Qu S, Hwang KC (2004) The atomic-scale finite element method. Comput Methods Appl Mech Eng 193(17–20):1849–1864. https://doi.org/10.1016/j.cma.2003.12.037

    Article  ADS  Google Scholar 

  7. Su W, Zhang Y, Wu L (2021) Multiscale simulation of molecular gas flows by the general synthetic iterative scheme. Comput Methods Appl Mech Eng, 373. https://doi.org/10.1016/j.cma.2020.113548

  8. Allen MP, Tildesley DJ (2017) Computer simulation of liquids. Oxford University Press, Oxford

    Book  Google Scholar 

  9. Atkins P, De Paula J, Keeler J (2018) Atkins’ physical chemistry. Oxford University Press, Oxford

    Google Scholar 

  10. Frenkel D, Smit B (2001) Understanding molecular simulation: from algorithms to applications, vol 1. Elsevier, Amsterdam

    Google Scholar 

  11. Rowlinson JS, Widom B (2013) Molecular theory of capillarity. Courier Corporation

  12. Tuckerman M (2010) Statistical mechanics: theory and molecular simulation. Oxford University Press, Oxford

    Google Scholar 

  13. Gao Y, Wang F, Zhu T, Zhao J (2010) Investigation on the mechanical behaviors of copper nanowires under torsion. Comput Mater Sci 49(4):826–830. https://doi.org/10.1016/j.commatsci.2010.06.031

    Article  CAS  Google Scholar 

  14. Gao Y, Wang H, Zhao J, Sun C, Wang F (2011) Anisotropic and temperature effects on mechanical properties of copper nanowires under tensile loading. Comput Mater Sci 50(10):3032–3037. https://doi.org/10.1016/j.commatsci.2011.05.023

    Article  CAS  Google Scholar 

  15. Jiang S, Chen Z, Gan Y, Oloriegbe SY, Sewell TD, Thompson DL (2012) Size effects on the wave propagation and deformation pattern in copper nanobars under symmetric longitudinal impact loading. J Phys D Appl Phys 45(47):475305

    Article  ADS  Google Scholar 

  16. Jiang S, Zhang H, Zheng Y, Chen Z (2009) Atomistic study of the mechanical response of copper nanowires under torsion. J Phys D Appl Phys 42(13):135408. https://doi.org/10.1088/0022-3727/42/13/135408

  17. Jiang S, Zhang H, Zheng Y, Chen Z (2010) Loading path effect on the mechanical behaviour and fivefold twinning of copper nanowires. J Phys D Appl Phys 43(33):335402. https://doi.org/10.1088/0022-3727/43/33/335402

  18. Koh SJA, Lee HP, Lu C, Cheng QH (2005) Molecular dynamics simulation of a solid platinum nanowire under uniaxial tensile strain: Temperature and strain-rate effects. Phys Rev B 72(8):085414. https://doi.org/10.1103/PhysRevB.72.085414

  19. Liang W, Zhou M (2004) Response of copper nanowires in dynamic tensile deformation. Proc Inst Mech Eng C J Mech Eng Sci 218(6):599–606. https://doi.org/10.1243/095440604774202231

    Article  CAS  Google Scholar 

  20. Wu HA (2004) Molecular dynamics simulation of loading rate and surface effects on the elastic bending behavior of metal nanorod. Comput Mater Sci 31(3–4):287–291. https://doi.org/10.1016/j.commatsci.2004.03.017

    Article  CAS  Google Scholar 

  21. Zhan HF, Gu YT (2012) Theoretical and numerical investigation of bending properties of Cu nanowires. Comput Mater Sci 55:73–80. https://doi.org/10.1016/j.commatsci.2011.12.024

    Article  CAS  Google Scholar 

  22. Zheng Y, Zhang H, Chen Z, Jiang S (2009) Deformation and stability of copper nanowires under bending. Int J Multiscale Comput Eng 7(3):205–215. https://doi.org/10.1615/IntJMultCompEng.v7.i3.40

    Article  CAS  Google Scholar 

  23. Bathe K-J (2006) Finite element procedures. Klaus-Jurgen Bathe, Englewood Cliffs

  24. Bathe KJ, Ramm E, Wilson EL (1975) Finite element formulations for large deformation dynamic analysis. Int J Numer Meth Eng 9(2):353–386

    Article  Google Scholar 

  25. Reddy JN (1993) An introduction to the finite element method. McGraw-Hill, New York

    Google Scholar 

  26. Sulsky D, Chen Z, Schreyer HL (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118(1–2):179–196. https://doi.org/10.1016/0045-7825(94)90112-0

    Article  ADS  MathSciNet  Google Scholar 

  27. Chen Z, Brannon RM (2002) An evaluation of the material point method. Sandia National Lab.(SNL-NM), Albuquerque, NM (United States); Sandia National Lab.(SNL-CA), Livermore, CA (United States).

  28. Zhang X, Chen Z, Liu Y (2016) The material point method: a continuum-based particle method for extreme loading cases. Academic Press, Cambridge

    Google Scholar 

  29. Andersen S, Andersen L (2010) Modelling of landslides with the material-point method. Comput Geosci 14(1):137–147. https://doi.org/10.1007/s10596-009-9137-y

    Article  Google Scholar 

  30. Bardenhagen SG, Kober EM (2004) The generalized interpolation material point method. Comput Model Eng Sci 5(6):477–496. https://doi.org/10.3970/cmes.2004.005.477

    Article  Google Scholar 

  31. Charlton TJ, Coombs WM, Augarde CE (2017) iGIMP: an implicit generalised interpolation material point method for large deformations. Comput Struct 190:108–125. https://doi.org/10.1016/j.compstruc.2017.05.004

    Article  Google Scholar 

  32. Nakano A, Bachlechner ME, Kalia RK, Lidorikis E, Vashishta P, Voyiadjis GZ, Campbell TJ, Ogata S, Shimojo F (2001) Multiscale simulation of nanosystems. Comput Sci Eng 3(4):56–66

    Article  CAS  Google Scholar 

  33. Su Y-C, Sewell T, Chen Z (2021) Comparative investigation of shear-band evolution using discrete and continuum-based particle methods. Acta Geotech. https://doi.org/10.1007/s11440-021-01150-8

    Article  Google Scholar 

  34. Su Y-C, Jiang S, Gan Y, Chen Z, Lu J-M (2019) Investigation of the mechanical responses of copper nanowires based on molecular dynamics and coarse-grained molecular dynamics. Comput Part Mech 6(2):177–190. https://doi.org/10.1007/s40571-018-0205-8

    Article  Google Scholar 

  35. Raabe D (2014) Recovery and recrystallization: phenomena, physics, models, simulation. Phys Metal, pp 2291–2397.

  36. Galliéro G, Boned C, Baylaucq A (2005) Molecular dynamics study of the Lennard–Jones fluid viscosity: application to real fluids. Ind Eng Chem Res 44(17):6963–6972

    Article  Google Scholar 

  37. Johnson RA (1988) Relationship between defect energies and embedded-atom-method parameters. Phys Rev B Condens Matter 37(11):6121–6125. https://doi.org/10.1103/physrevb.37.6121

    Article  ADS  CAS  PubMed  Google Scholar 

  38. Johnson RA (1989) Alloy models with the embedded-atom method. Phys Rev B Condens Matter 39(17):12554–12559. https://doi.org/10.1103/physrevb.39.12554

    Article  ADS  CAS  PubMed  Google Scholar 

  39. Mishin Y, Mehl M, Papaconstantopoulos D, Voter A, Kress J (2001) Structural stability and lattice defects in copper: ab initio, tight-binding, and embedded-atom calculations. Phys Rev B 63(22):224106. https://doi.org/10.1103/PhysRevB.63.224106

  40. Chen Z, Han Y, Jiang S, Gan Y, Sewell TD (2012) A multiscale material point method for impact simulation. Theor Appl Mech Lett 2(5). https://doi.org/10.1063/2.1205103

  41. Gu YT, Zhang LC (2006) A concurrent multiscale method based on the meshfree method and molecular dynamics analysis. Multiscale Model Simul 5(4):1128–1155. https://doi.org/10.1137/060654232

    Article  MathSciNet  CAS  Google Scholar 

  42. Tong Q, Li S (2015) From molecular systems to continuum solids: a multiscale structure and dynamics. J Chem Phys 143(6):064101. https://doi.org/10.1063/1.4927656

  43. Hull D, Bacon DJ (2001) Introduction to dislocations. Butterworth-Heinemann, Oxford

    Google Scholar 

  44. Plimpton S (1995) Fast parallel algorithms for short-range molecular dynamics. J Comput Phys 117(1):1–19. https://doi.org/10.2172/10176421

    Article  ADS  CAS  Google Scholar 

  45. Thompson AP, Aktulga HM, Berger R, Bolintineanu DS, Brown WM, Crozier PS, in 't Veld PJ, Kohlmeyer A, Moore SG, Nguyen TD, Shan R, Stevens MJ, Tranchida J, Trott C, Plimpton SJ (2022) LAMMPS—a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales. Comput Phys Commun, 271. https://doi.org/10.1016/j.cpc.2021.108171

  46. Tsuzuki H, Branicio PS, Rino JP (2007) Structural characterization of deformed crystals by analysis of common atomic neighborhood. Comput Phys Commun 177(6):518–523. https://doi.org/10.1016/j.cpc.2007.05.018

    Article  ADS  CAS  Google Scholar 

  47. Stukowski A (2010) Visualization and analysis of atomistic simulation data with OVITO–the Open Visualization Tool. Model Simulat Mater Sci Eng 18(1):015012. https://doi.org/10.1088/0965-0393/18/1/015012

  48. Chen Z, Schreyer H (1994) On nonlocal damage models for interface problems. Int J Solids Struct 31(9):1241–1261. https://doi.org/10.1016/0020-7683(94)90119-8

    Article  Google Scholar 

  49. Kanel G, Razorenov S, Savinykh A, Rajendran A, Chen Z (2005) A study of the failure wave phenomenon in glasses compressed at different levels. J Appl Phys 98(11):113523. https://doi.org/10.1063/1.2139829

  50. Chen Z (1996) Continuous and discontinuous failure modes. J Eng Mech 122(1):80–82. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:1(80)

    Article  Google Scholar 

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Acknowledgements

This work was supported in part by the National Science and Technology Council of Taiwan under the contract number NSTC 110-2222-E-008-009-MY2. Y.C. Su also appreciates the computational time and resources as obtained from National Center for High-Performance Computing, Taiwan.

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Su, YC., Chen, Z. Study of the shear-band evolution across the interface between different spatial scales. Comp. Part. Mech. 11, 73–88 (2024). https://doi.org/10.1007/s40571-023-00609-7

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