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Temporal Acceleration in Coupled Continuum-Atomistic Methods

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Abstract

In order to speed up molecular simulations, coupled continuum-atomistic methods have been developed in which atomistic resolution is only retained in regions of interest with the rest of the model approximated as a continuum. In parallel, there have been efforts to extend the time scale accessible in molecular simulations by filtering out atomic vibrations and focusing on the more interesting dynamics associated with the formation and motion of defects. This article focuses on a current research trend to combine these two complementary approaches into a unified framework that can simultaneously span multiple length and time scales from the microscopic to the macroscopic. As a specific example, the combination of the spatial quasicontinuum (QC) method with the temporal hyperdynamics method to create “hyper-QC” is described.

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References

  • Curtin WA, Miller RE (2003) Atomistic/continuum coupling methods in multi-scale materials modeling. Model Simul Mater Sci Eng 11:R33–R68

    Article  ADS  Google Scholar 

  • Dupuy LM, Tadmor EB, Miller RE, Phillips R (2005) Finite temperature quasicontinuum: molecular dynamics without all the atoms. Phys Rev Lett 95:060202

    Article  ADS  Google Scholar 

  • Germann TC, Kadau K (2008) Trillion-atom molecular dynamics becomes a reality. Int J Mod Phys C 19:1315–1319

    Article  ADS  Google Scholar 

  • Gnecco E, Bennewitz R, Gyalog T, Loppacher C, Bammerlin M, Meyer E, Güntherodt HJ (2000) Velocity dependence of atomic friction. Phys Rev Lett 84:1172–1175

    Article  ADS  Google Scholar 

  • Henkelman G, Jónsson H (2001) Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J Chem Phys 115:9657–9666

    Article  ADS  Google Scholar 

  • Jaynes ET (1957a) Information theory and statistical mechanics. Part I. Phys Rev 106:620–630

    Article  ADS  MathSciNet  Google Scholar 

  • Jaynes ET (1957b) Information theory and statistical mechanics. Part II. Phys Rev 108:171–190

    Article  ADS  MathSciNet  Google Scholar 

  • Kim WK, Falk ML (2010) Accelerated molecular dynamics simulation of low-velocity frictional sliding. Model Simul Mater Sci Eng 18:034003

    Article  ADS  Google Scholar 

  • Kim WK, Tadmor EB (2017) Accelerated quasicontinuum: a practical perspective on hyper-QC with application to nanoindentation. Philos Mag 97:2284–2316

    Article  ADS  Google Scholar 

  • Kim WK, Luskin M, Perez D, Voter AF, Tadmor EB (2014) Hyper-QC: an accelerated finite-temperature quasicontinuum method using hyperdynamics. J Mech Phys Solids 63:94–112

    Article  ADS  Google Scholar 

  • Kirkwood JG (1935) Statistical mechanics of fluid mixtures. J Chem Phys 3:300–313

    Article  ADS  Google Scholar 

  • Knap J, Ortiz M (2001) An analysis of the quasicontinuum method. J Mech Phys Solids 49: 1899–1923

    Article  ADS  Google Scholar 

  • Kulkarni Y, Knap J, Ortiz M (2008) A variational approach to coarse graining of equilibrium and non-equilibrium atomistic description at finite temperature. J Mech Phys Solids 56:1417–1449

    Article  ADS  MathSciNet  Google Scholar 

  • Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci USA 99: 12562–12566

    Article  ADS  Google Scholar 

  • LeSar R, Najafabadi R, Srolovitz D (1989) Finite-temperature defect properties from free-energy minimization. Phys Rev Lett 63:624–627

    Article  ADS  Google Scholar 

  • Li J, Sarkar S, Cox WT, Lenosky TJ, Bitzek E, Wang Y (2011) Diffusive molecular dynamics and its application to nanoindentation and sintering. Phys Rev B 84:054103

    Article  ADS  Google Scholar 

  • Miller RE, Tadmor EB (2002) The quasicontinuum method: overview, applications, and current directions. J Comput Aided Mater Des 9:203–239

    Article  ADS  Google Scholar 

  • Miller RE, Tadmor EB (2009) A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Model Simul Mater Sci Eng 17:053001

    Article  ADS  Google Scholar 

  • Miron RA, Fichthorn KA (2003) Accelerated molecular dynamics with the bond-boost method. J Chem Phys 119:6210–6216

    Article  ADS  Google Scholar 

  • Ponga M, Ortiz M, Ariza M (2015) Finite-temperature non-equilibrium quasi-continuum analysis of nanovoid growth in copper at low and high strain rates. Mech Mater 90:253–267

    Article  Google Scholar 

  • Ponga M, Ramabathiran AA, Bhattacharya K, Ortiz M (2016) Dynamic behavior of nano-voids in magnesium under hydrostatic tensile stress. Model Simul Mater Sci Eng 24:065003

    Article  ADS  Google Scholar 

  • Shenoy VB, Miller R, Tadmor EB, Rodney D, Phillips R, Ortiz M (1999) An adaptive finite element approach to atomic-scale mechanics: the quasicontinuum method. J Mech Phys Solids 47: 611–642

    Article  ADS  MathSciNet  Google Scholar 

  • Sørensen MR, Voter AF (2000) Temperature-accelerated dynamics for simulation of infrequent events. J Chem Phys 112:9599–9606

    Article  ADS  Google Scholar 

  • Tadmor EB, Miller RE (2011) Modeling materials: continuum, atomistic and multiscale techniques. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Philos Mag A 73:1529–1563

    Article  ADS  Google Scholar 

  • Tadmor EB, Smith GS, Bernstein N, Kaxiras E (1999) Mixed finite element and atomistic formulation for complex cystals. Phys Rev B 59:235–245

    Article  ADS  Google Scholar 

  • Tadmor EB, Legoll F, Kim WK, Dupuy LM, Miller RE (2013) Finite-temperature quasi-continuum. Appl Mech Rev 65:010803

    Article  ADS  Google Scholar 

  • Tomlinson GA (1929) A molecular theory of friction. Philos Mag 7:905–939

    Article  Google Scholar 

  • Vanden-Eijnden E, Tal FA (2005) Transition state theory: variational formulation, dynamical corrections, and error estimates. J Chem Phys 123:184103

    Article  ADS  Google Scholar 

  • Venturini G, Wang K, Romero I, Ariza MP, Ortiz M (2014) Atomistic long-term simulation of heat and mass transport. J Mech Phys Solids 73:242–268

    Article  ADS  MathSciNet  Google Scholar 

  • Voter AF (1997) A method for accelerating the molecular dynamics simulation of infrequent events. J Chem Phys 106:4665–4667

    Article  ADS  Google Scholar 

  • Voter AF (1998) Parallel replica method for dynamics of infrequent events. Phys Rev B 57: 13985–13988

    Article  ADS  Google Scholar 

  • Voter AF (2005) Introduction to the Kinetic Monte Carlo method. In: Sickafus KE, Kotomin EA (eds) Radition effects in solids. Springer, NATO Publishing Unit, Dordrecht

    Google Scholar 

  • Zhou XW, Johnson RA, Wadley HNG (2004) Misfit-energy-increasing dislocations in vapor-deposited CoFe/NiFe multilayers. Phys Rev B 69:144113

    Article  ADS  Google Scholar 

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Acknowledgements

WKK and EBT were supported in part by the National Science Foundation (NSF) through a collaborative research grant under Award Numbers CMMI-1463038 and CMMI-1462807, respectively.

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Authors and Affiliations

  1. Department of Mechanical and Materials Engineering, University of Cincinnati, Cincinnati, OH, USA

    Woo Kyun Kim

  2. Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN, USA

    Ellad B. Tadmor

Authors
  1. Woo Kyun Kim
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  2. Ellad B. Tadmor
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Corresponding author

Correspondence to Ellad B. Tadmor .

Editor information

Editors and Affiliations

  1. Institute of Physics, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Wanda Andreoni

  2. Department of Nuclear Science & Engineering , Massachusetts Institute of Technology , Cambridge, MA, USA

    Sidney Yip

Section Editor information

  1. Theoretical Division T-1, Los Alamos National Laboratory, Los Alamos, NM, USA

    Danny Perez

  2. Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, New Mexico, USA

    Blas Pedro Uberuaga

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Kim, W.K., Tadmor, E.B. (2018). Temporal Acceleration in Coupled Continuum-Atomistic Methods. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_26-1

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  • DOI: https://doi.org/10.1007/978-3-319-42913-7_26-1

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42913-7

  • Online ISBN: 978-3-319-42913-7

  • eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics

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