An adaptive concurrent multiscale method for the dynamic simulation of dislocations

International Journal for Numerical Methods in Engineering

Volumn 86, Issue 4-5, 2011, Pages 575-597

  Gracie, Robert ^a   Belytschko, Ted ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b Northwestern University   (United States)

Author keywords

Adaptivity; Bridging domain method; Continuum; Dislocations; Extended finite element method; Molecular dynamics; Multiscale

Indexed keywords

ADAPTIVITY; BRIDGING DOMAIN METHOD; CONTINUUM; DISLOCATIONS; EXTENDED FINITE ELEMENT METHOD; MULTISCALES;

COARSENING; COMPUTER SIMULATION; CONTINUUM MECHANICS; CRACK PROPAGATION; CRACK TIPS; EDGE DISLOCATIONS; MOLECULAR DYNAMICS; REFINING;

FINITE ELEMENT METHOD;

EID: 79953075608     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.3112     Document Type: Article

References (33)

1. Gracie R, Belytschko T. Concurrently coupled atomistic and XFEM models for dislocations and cracks. International Journal for Numerical Methods in Engineering 2008; 78(3):354-378.
2. LP Kubin, Canova G. The modelling of dislocation patterns. Scripta Metallurgica et Materialia 1992; 27(8):957-962.
3. Abraham FF, Walkup HJ, Gao R, Duchaineau M, Diaz De La Rubia T, Seager M. Simulating materials failure by using up to one billion atoms and the world's fastest computer: work-hardening. Proceedings of the National Academy of Sciences of the U.S.A. 2002; 99(9):5777-5782.
4. Ghoniem NM, Tong S-H, Sun LZ. Parametric dislocation dynamics: a thermodynamics-based approach to investigations of mesoscopic plastic deformation. Physical Review B 2000; 61(2):913-927. DOI: 10.1103/PhysRevB.61.913.
5. Schwarz KW. Simulation of dislocations on the mesoscopic scale. i. methods and examples. Journal of Applied Physics 1999; 85(1):108-119.
6. Bulatov VV, Cai W. Computer Simulations of Dislocations (1st edn). Oxford University Press: Oxford, 2006.
7. Hirth JP, Lothe J. Theory of Dislocations, vol. 1 (2nd edn). Wiley: New York, 1982.
8. Han X, Ghoniem NM. Stress field and interaction forces of dislocations in anisotropic multilayer thin films. Philosophical Magazine 2005; 85(11):1205-1225.
9. Gracie R, Ventura G, Belytschko T. A new fast method for dislocations based on interior discontinuities. International Journal for Numerical Methods in Engineering 2007; 69:423-441.
10. Gracie R, Oswald J, Belytschko T. On a new extended finite element method for dislocations: core enrichments. Journal of the Mechanics and Physics of Solids 2008; 56:200-214. DOI: 10.1016/j.jmps.2007.07.010.
11. Takahashi A, Ghoniem NM. A computational method for dislocation-precipitate interaction. Journal of the Mechanics and Physics of Solids 2008; 56(4):1534-1553.
12. Tadmor EB, Ortiz M, Philips R. Quasicontinuum analysis of defects in solids. Philosophical Magazine A 1996; 73(6):1529-1563.
13. Abraham FF, Broughton JQ, Bernstein N, Kaxiras E. Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhysics Letters 1998; 44(6):783-787.
14. Xiao SP, Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering 2004; 193:1645-1669.
15. Wagner GJ, Karpov EG, Liu WK. Molecular dynamics boundary conditions for regular crystal lattices. Computer Methods in Applied Mechanics and Engineering 2004; 193(17-20):1579-1601.
16. Miller RE, Tadmor EB. A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Modelling and Simulation in Materials Science and Engineering 2009; 17:053001.
17. Xu M, Gracie R, Belytschko T. Concurrent coupling of atomistic and continuum models, multiscale methods. In Multiscale Methods-Bridging the Scales in Science and Engineering, Fish J (ed.). Oxford Press: Oxford, 2009; 93-133.
18. Shilkrot LE, Miller RE, Curtin WA. Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics. Journal of the Mechanics and Physics of Solids 2004; 52(4):755-787.
19. Shilkrot LE, Curtin WA, Miller RE. A coupled atomistic/continuum model of defects in solids. JMPS 2002; 50(10):2085-2105.
20. van der Giessen E, Needleman A. Discrete dislocation plasticity: a simple planar model. Modelling Simulation in Material Science and Engineering 1995; 3:689-735.
21. Gracie R, Belytschko T. An extended bridging domain method for continuum-atomistic simulations of discontinuities. World Congress on Computation Mechanics, Venice, Italy, July 2008.
22. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50:993-1013.
23. Gravouil A, Moes N, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets-Part II: Level set update. International Journal for Numerical Methods in Engineering 2002; 53:2569-2586.
24. Johnson RA. Relationship between two-body interatomic potentials in a lattice model and elastic constants. Physical Review B 1972; 6(6):2094-2100.
25. Murray Daw S, Baskes MI. Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals. Physical Review B 1984; 29(12):6443-6453.
26. Wolf D, Lutsko JF. Structurally-induced elastic anomalies in a superlattice of (0 0 1) twist grain boundaries. Journal of Materials Research 1989; 4(6):1427-1443.
27. Xu M, Gracie R, Belytschko T. A continuum-to-atomistic bridging domain method for composite lattices. International Journal for Numerical Methods in Engineering 2010; 81(13):1635-1658.
28. Klein P. A virtual internal bond approach to modeling crack nucleation and growth. Ph.D. Thesis, Stanford University, 1999.
29. Xiang Y, Srolovitz DJ, Cheng LT, Weinan E. Level set simulations of dislocation-particle bypass mechanisms. Acta Materialia 2004; 52(7):1745-1760.
30. Xu M, Belytschko T. Conservation properties of the bridging domain method for coupled molecular/continuum dynamics. International Journal for Numerical Methods in Engineering 2008; 76(3):278-294. DOI: 10.1002/nme.2323.
31. Berendsen HJC, Postma JPM, Van Gunsteren WF, DiNola A, Haak JR. Molecular dynamics with coupling to an external bath. The Journal of Chemical Physics 1984; 81:3684.
32. Prudhomme S, Ben Dhia H, Bauman PT, Elkhodja N, Oden JT. Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method. Computer Methods in Applied Mechanics and Engineering 2008; 197(41-42):3399-3409.
33. Li J. AtomEye: atomistic configuration viewer. Modelling and Simulation in Materials Science and Engineering 2003; 11:173-177.