Coupling of atomistic and continuum simulations using a bridging scale decomposition

Journal of Computational Physics

Volumn 190, Issue 1, 2003, Pages 249-274

  Wagner, Gregory J ^a,b   Liu, Wing Kam ^a  

^a Northwestern University   (United States)

^b SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Bridging scale; Coupling methods; Finite elements; Molecular dynamics; Multiple scale simulations

Indexed keywords

CONTINUUM MECHANICS; FINITE ELEMENT METHOD; KINETIC ENERGY; KINETICS;

ATOMISTIC SIMULATIONS; BRIDGING SCALE; CONTINUUM SIMULATIONS; COUPLING METHODS; FINITE ELEMENT; MECHANICS SIMULATIONS; MOLECULAR DYNAMICS SOLUTIONS; MULTIPLE SCALE; MULTIPLE-SCALE SIMULATION; SHAPE FUNCTIONS;

MOLECULAR DYNAMICS;

EID: 0042858270     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00273-0     Document Type: Article

References (32)

1. P. Gumbsch, R.M. Cannon, Atomistic aspects at brittle fracture, MRS Bull. 25 (5) (2000) 15-20.
2. M.H. Muser, Towards an atomistic understanding of solid friction by computer simulations, Comput. Phys. Commun. 146 (1) (2002) 54-62.
3. M.F. Horstemeyer, M.I. Baskes, S.J. Plimpton, Computational nanoscale plasticity simulations using embedded atom potentials, Theor. Appl. Fract. Mech. 37 (1-3) (2001) 49-98.
4. F.F. Abraham, J.Q. Broughton, N. Bernstein, E. Kaxiras, Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture, Europhys. Lett. 44 (6) (1998) 783-787.
5. J.Q. Broughton, F.F. Abraham, N. Bernstein, E. Kaxiras, Concurrent coupling of length scales: methodology and application, Phys. Rev. B 60 (4) (1999) 2391-2403.
6. E.B. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids, Philos. Mag. A 73 (6) (1996) 1529-1563.
7. E.B. Tadmor, R. Phillips, M. Ortiz, Mixed atomistic and continuum models of deformation in solids, Langmuir 12 (19) (1996) 4529-4534.
8. V.B. Shenoy, R. Miller, E.B. Tadmor, R. Phillips, M. Ortiz, Quasicontinuum models of interfacial structure and deformation, Phys. Rev. Lett. 80 (4) (1998) 742-745.
9. R. Miller, M. Ortiz, R. Phillips, V. Shenoy, E.B. Tadmor, Quasicontinumn models of fracture and plasticity, Eng. Fract. Mech. 61 (3-4) (1998) 427-444.
10. R. Miller, E.B. Tadmor, R. Phillips, M. Ortiz, Quasicontinuum simulation of fracture at the atomic scale, Model Simulat. Mater. Sci. 6 (5) (1998) 607-638.
11. M. Ortiz, A.M. Cuitino, J. Knap, M. Koslowski, Mixed atomistic continuum models of material behavior: the art of transcending atomistics and informing continua, MRS Bull. 26 (3) (2001) 216-221.
12. V. Shenoy, R. Phillips, Finite temperature quasicontinuum methods, in: V. Bulatov, T.d.1 Rubia, R. Phillips, E. Kaxiras, N. Ghoniem (Eds.), Multiscale Modelling of Materials, Materials Research Society, Warrendale, PA, 1999, pp. 465-471.
13. S. Li, W.K. Liu, Meshfree and particle methods and their applications, Appl. Mech. Rev. 55 (1) (2002) 1-34.
14. T.J.R. Hughes, G.R. Feijoo, L. Mazzei, J.B. Quincy, The variational multiscale method - a paradigm for computational mechanics, Comput. Meth. Appl. Mech. Eng. 166 (1-2) (1998) 3-24.
15. K. Garikipati, T.J.R. Hughes, A variational multiscale approach to strain localization - formulation for multidimensional problems, Comput. Meth. Appl. Mech. Eng. 188 (1-3) (2000) 39-60.
16. W.K. Liu, R.A. Uras, Y. Chen, Enrichment of the finite element method with the reproducing kernel particle method, J. Appl. Mech-T ASME 64 (4) (1997) 861-870.
17. G.J. Wagner, W.K. Liu, Hierarchical enrichment for bridging scales and mesh-free boundary conditions, Int. J. Numer. Meth. Eng. 50 (3) (2001) 507-524.
18. W.M. Han, G.J. Wagner, W.K. Liu, Convergence analysis of a hierarchical enrichment of dirichlet boundary conditions in a mesh-free method, Int. J. Numer. Meth. Eng. 53 (6) (2002) 1323-1336.
19. S.A. Adelman, J.D. Doll, Generalized langevin equation approach for atom/solid-surface scattering - collinear atom/harmonic chain model, J. Chem. Phys. 61 (10) (1974) 4242-4245.
20. S.A. Adelman, J.D. Doll, Generalized langevin equation approach for atom-solid-surface scattering - general formulation for classical scattering off harmonic solids, J. Chem. Phys. 64 (6) (1976) 2375-2388.
21. H.J.C. Berendsen, J.P.M. Postma, W.F. Vangunsteren, A. Dinola, J.R. Haak, Molecular-dynamics with coupling to an external bath, J. Chem. Phys. 81 (8) (1984) 3684-3690.
22. W. Cai, M. de Koning, V.V. Bulatov, S. Yip, Minimizing boundary reflections in coupled-domain simulations, Phys. Rev. Lett. 85 (15) (2000) 3213-3216.
23. W. E, Z.Y. Huang, Matching conditions in atomistic-continuum modeling of materials, Phys. Rev. Lett. 87 (13) (2001), art. no. 135501.
24. G.J. Wagner, E. Karpov, W.K. Liu, Molecular dynamics boundary conditions for regular crystal lattices, Comput. Meth. Appl. Mech. Eng., in press.
25. C. Farhat, M. Lesoinne, Two efficient staggered algorithms for the serial and parallel solution of three-dimensional nonlinear transient aeroelastic problems, Comput. Meth. Appl. Mech. Eng. 182 (3-4) (2000) 499-515.
26. T. Belytschko, H. Yen, R. Mullen, Mixed methods for time integration, Comput. Meth. Appl. Mech. Eng. 17-8 (1979) 259-275.
27. W.K. Liu, T. Belytschko, Mixed-time implicit-explicit finite-elements for transient analysis, Comput. Struct. 15 (4) (1982) 445-450.
28. W.K. Liu, Development of mixed time partition procedures for thermal-analysis of structures, Int. J. Numer. Meth. Eng. 19 (1) (1983) 125-140.
29. J.M. Haile, Molecular Dynamics Simulation: Elementary Methods, Wiley, New York, 1992.
30. D. Qian, Multiscale simulation of the mechanics of carbon nanotubes, Ph.D. Thesis, Northwestern University, 2002.
31. D. Qian, G.J. Wagner, W.K. Liu, A multicale projection method for the analysis of carbon nanotubes, in press.
32. F. Reif, Fundamentals of Statistical and Thermal Physics, McGraw-Hill, New York, 1965.