Variational boundary conditions for molecular dynamics simulations: Treatment of the loading condition

Journal of Computational Physics

Volumn 227, Issue 24, 2008, Pages 10078-10093

  Li, Xiantao ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

MOLECULAR DYNAMICS; NUMERICAL METHODS; TEMPERATURE;

APPROXIMATE BOUNDARY CONDITION; DYNAMICS SIMULATION; EXTERNAL LOADING; FINITE TEMPERATURES; HEAT BATH; LATTICE GREEN FUNCTION; LOADING CONDITION; LOWS-TEMPERATURES; MORI-ZWANZIG; TEMPERATURE TREATMENTS;

BOUNDARY CONDITIONS;

EID: 54349088921     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2008.08.010     Document Type: Article

References (44)

1. Adelman S.A., and Doll J.D. Generalized Langevin equation approach for atom/solid-surface scattering: collinear atom/harmonic chain model. J. Chem. Phys. 61 (1974) 4242
2. Adelman S.A., and Doll J.D. Generalized Langevin equation approach for atom/solid-surface scattering: general formulation for classical scattering off harmonic solids. J. Chem. Phys. 64 (1976) 2375
3. Andersen H.C. Molecular dynamics simulations at constant pressure and/or temperature. J. Chem. Phys. 72 (1980) 2384-2393
4. Ashcroft N.W., and Mermin N.D. Solid State Physics (1976), Brooks Cole
5. B.J. Berne, R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics, Dover Publication, 2000.
6. Cai W., de Koning M., Bulatov V.V., and Yip S. Minimizing boundary reflections in coupled-domain simulations. Phys. Rev. Lett. 85 (2000) 3213
7. Cheung K.S., and Yip S. A molecular-dynamics simulation of crack-tip extension: the brittle-to-ductile transition. Model. Simul. Mater. Sci. Eng. 2 (1994) 865-892
8. Chorin A.J., Hald O.H., and Kupferman R. Optimal prediction and the Mori-Zwanzig representation of irreversible processes. Proc. Natl. Acad. Sci. USA 97 (2000) 6253-6257
9. Chorin A.J., Hald O.H., and Kupferman R. Optimal prediction with memory. Physica D 166 (2002) 239-257
10. Chorin A.J., Kast A., and Kupferman R. Optimal prediction of underresolved dynamics. Proc. Natl. Acad. Sci. USA 96 (1998) 4094-4098
11. Chorin A.J., and Stinis P. Problem reduction, renormalization, and memory. Commun. Appl. Math. Comp. Sci. 1 (2005) 1-27
12. Daw M.S., and Baskes M.I. Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Phys. Rev. B 29 (1984) 6443
13. E W., and Huang Z. Matching conditions in atomistic-continuum modeling of material. Phys. Rev. Lett. 87 (2001) 135501
14. E W., and Huang Z. A dynamic atomistic-continuum method for the simulation of crystalline material. J. Comput. Phys. 182 (2002) 234-261
15. E W., and Ming P. Cauchy-Born rule and the stability of the crystalline solids: dynamic problems. Acta Math. Appl. Sin. Engl. Ser. 23 (2007) 529-550
16. J.L. Ericksen, The Cauchy-Born hypothesis for crystals, in: M. Gurtin (Ed.), Phase Transformations and Material Instabilities in Solids, 1984.
17. Frenkel D., and Smit B. Understanding Molecular Simulation: From Algorithms to Applications. second ed. (2002), Academic Press
18. Gill S.P.A., Jia Z., Leimkuhler B., and Cocks A.C.F. Rapid thermal equilibration in coarse-grained molecular dynamics. Phys. Rev. B 73 (2006) 184304
19. Holian B.L., and Ravelo R. Fracture simulation using large-scale molecular dynamics. Phys. Rev. B 51 (1995) 11275
20. Holland D., and Mardar M. Cracks and atoms. Adv. Mater. 11 (1999) 793-806
21. Hoover W.G. Constant-pressure equations of motion. Phys. Rev. A 34 (1986) 2499-2500
22. Karpov E.G., Park H.S., and Liu W.K. A phonon heat bath approach for the atomistic and multiscale simulation of solids. Int. J. Numer. Methods Eng. 70 (2007) 351-378
23. Karpov E.G., Wagner G.J., and Liu W.K. A Green's function approach to deriving non-reflecting boundary conditions in molecular dynamics simulations. Int. J. Numer. Methods Eng. 62 9 (2005) 1250-1262
24. Kubo R. The fluctuation-dissipation theorem. Reports Progress Phys. 29 1 (1966) 255-284
25. X. Li, Stability of the Boundary Conditions for Molecular Dynamics, preprint submitted.
26. Li X., and E W. Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Commum. Comput. Phys. 1 (2006) 136-176
27. Li X., and E W. Boundary conditions for molecular dynamics simulations at finite temperature: treatment of the heat bath. Phys. Rev. B 76 (2007) 104107
28. Machova A., and Ackland G.J. Dynamic overshoot in α-iron by atomistic simulations. Model. Simul. Mater. Sci. Eng. 6 (1998) 521-542
29. Martyna G., Tuckerman M., Tobias D., and Klein M. Explicit reversible integration algorithms for extended systems. Molecul. Phys. 87 (1996) 1117
30. Melchionna S., Ciccotti G., and Holian B.L. Hoover NPT dynamics for systems varying in shape and size. Molecul. Phys. 78 (1993) 533-544
31. Miller R., Tadmor E.B., Phillips R., and Ortiz M. Quasicontinuum simulation of fracture at the atomic scale. Model. Simul. Mater. Sci. Eng. 6 (1998) 607-638
32. Mori H. Transport, collective motion, and Brownian motion. Prog. Theor. Phys. 33 (1965) 423-450
33. Needleman A. Numerical modeling of crack growth under dynamic loading conditions. Comput. Mech. 19 (1997) 463-469
34. Parrinello M., and Rahman A. Polymorphic transition in single crystals: A new molecular dynamics method. J. Appl. Phys. 52 (1981) 7182
35. V. Shastry, D. Farkas, Molecular statics simulation of crack propagation in alpha-Fe using EAM potentials, in: Materials Research Society Symposium Proceedings, Boston, MA, United States, November 27-December 1, 1995, 1996, pp. 75-80.
36. Sih G.C., and Liebowitz H. Fracture, An Advanced Treatise (1968), Academic Press
37. Stroh A. Dislocations and cracks in anisotropic elasticity. Philos. Mag. 7 (1958) 625-646
38. Tadmor E.B., Ortiz M., and Phillips R. Quasicontinuum analysis of defects in crystals. Phil. Mag. A 73 (1996) 1529-1563
39. To A.C., and Li S. Perfectly matched multiscale simulations. Phys. Rev. B 72 (2005) 035414
40. Wagner G.J., Karpov E.G., and Liu W.K. Molecular dynamics boundary conditions for regular crystal lattice. Comput. Method Appl. Mech. Eng. 193 (2004) 1579-1601
41. Yang J.Z., and Li X. Boundary conditions for molecular dynamics simulations of solids: a comparative study. Phys. Rev. B 73 (2006) 224111
42. Zwanzig R. Collision of a gas atom with a cold surface. J. Chem. Phys. 32 (1960) 1173
43. Zwanzig R. Problems in nonlinear transport theory. In: Garrido L. (Ed). Systems Far From Equilibrium (1980), Interscience, New York
44. Zwanzig R. Nonequilibrium Statistical Mechanics (2001), Oxford University Press