Mixed Atomistic–Continuum Models:Transcending Atomistics and Informing Continua
3. R.E. Cohen, L. Stixrude, and E. Wasserman,
Phys. Rev. B: Condens. Matter 56 (14) (1997)
p. 8575.
4. P. Soderlind and J.A. Moriarty, Phys. Rev. B:
Condens. Matter 57 (17) (1998) p. 10340.
5. G. Steinle-Neumann, L. Stixrude, and R.E.
Cohen, Phys. Rev. B: Condens. Matter 60 (2) (1999)
p. 791.
Bulatov, T. Diaz de la Rubia, R. Phillips, E. Kaxiras,
and N. Ghoniem (Mater. Res. Soc. Symp. Proc.
538, Warrendale, PA, 1999) p. 465.
31. F. Ercolessi and J.B. Adams, Europhys. Lett.
26 (8) (1994) p. 583.
32. W. Zielinski, H. Huang, S. Venkataraman,
and W.W. Gerberich, Philos. Mag. A 72 (1995)
p. 1221.
33. W.W. Gerberich, J.C. Nelson, E.T. Lilleodden,
P. Anderson, and J.T. Wyrobek, Acta Mater. 44
(1996) p. 3585.
34. W.D. Nix, Mater. Sci. Eng., A 234 (1997) p. 37.
35. A. Gouldstone, H.J. Koh, K.Y. Zeng, A.E.
Giannakopoulos, and S. Suresh, Acta Mater. 48
(9) (2000) p. 227.
36. J. Belak, D.B. Boersker, and I.F. Stowers,
MRS Bull. XVIII (5) (1993) p. 55.
37. C.L. Kelchner, S.J. Plimpton, and J.C.
Hamilton, Phys. Rev. B 58 (17) (1998) p. 11085.
38. R.A. Johnson, Phys. Rev. B 37 (1988) p. 3924.
39. R.A. Johnson, Phys. Rev. B 39 (1989)
p. 12554.
40. M. Tang, L.P. Kubin, and G.R. Canova, Acta
Mater. 46 (9) (1998) p. 3221.
stress of screws in Ta, which is in the ex-
pected range.
The strength of dislocation jogs and
junctions has recently been computed
using atomistic and continuum mod-
els.15,24,43–45,49 Thus, for instance, Rodney
and Phillips24 used the quasi-continuum
method to simulate three-dimensional
Lomer–Cottrell junctions and determined
that this type of junction may be unzipped
under stress. Interestingly, Shenoy et al.49
subsequently showed that essentially
identical results may be obtained with an
anisotropic elastic model, provided that
dislocation dissociation into partials is ac-
counted for, which attests to the predictive
power of informed continuum models.
Shenoy et al.49 went on to map out the
complete stress–strength diagram for junc-
tions, that is, the locus of points in stress
space corresponding to the dissolution of
the junction. Likewise, Wang et al.43,44
have exhaustively cataloged the jogs and
kinks of bcc crystals and computed their
structures and energies.
6. R.E. Cohen, O. Gulseren, and R.J. Hemley,
Am. Mineral. 85 (2) (2000) p. 338.
7. T. Mura, Micromechanics of Defects in Solids
(Kluwer Academic Publishers, Boston, 1987).
8. M.I. Baskes, R.G. Hoagland, and A. Needle-
man, Mater. Sci. Eng., A 159 (1992) p. 1.
9. P.R. Dawson, A. Needleman, and S. Suresh,
Mater. Sci. Eng., A 175 (1994) p. 43.
10. M. Ortiz and C.F. Shih, eds., in Proc. IUTAM
Symp. on Computational Mechanics of Materials,
published in Model. Simul. Mater. Sci. Eng. 2 (34)
(May 1994) p. 421.
11. G.H. Campbell, S.M. Foiles, H.C. Huang, D.A.
Hughes, W.E. King, D.H. Lassila, D.J. Nikkel, T.
Diaz de la Rubia, J.Y. Shu, and V.P. Smyshlyaev,
Mater. Sci. Eng., A 251 (12) (1998) p. 1.
12. V.V. Bulatov and L.P. Kubin, Curr. Opin.
Solid State Mater. Sci. 3 (6) (1998) p. 558.
13. R. Phillips, Curr. Opin. Solid State Mater. Sci.
3 (6) (1998) p. 526.
41. M. Tang, B. Devincre, and L.P. Kubin,
Model. Simul. Mater. Sci. Eng. 7 (5) (1999) p. 893.
42. W. Xu and J.A. Moriarty, Comput. Mater. Sci.
9 (3–4) (1998) p. 348 .
Other similar studies, too numerous to
cite here, are available in the literature.
The substantial body of data that these
studies yield may be used to inform con-
tinuum models—for example, as material
constants or interaction rules in disloca-
tion dynamics codes (see References 12,
40, 41, 50, and 51).
14. M. Ortiz and R. Phillips, Adv. Appl. Mech. 36
(1999) p. 1.
15. R. Phillips, D. Rodney, V. Shenoy, E. Tadmor,
and M. Ortiz, Model. Simul. Mater. Sci. Eng. 7
(5) (1999) p. 769.
16. J.A. Moriarty, W. Xu, P. Soderlind, J. Belak,
L.H. Yang, and J. Zhu, Trans. ASME J. Eng. Mater.
Technol. 121 (2) (1999) p. 120.
17. M.I. Baskes, Curr. Opin. Solid State Mater.
Sci. 4 (3) (1999) p. 273.
18. R. Phillips, Crystals, Defects and Microstruc-
tures: Modeling across Scales (Cambridge Univer-
sity Press, Cambridge, 2000).
19. E.B. Tadmor, M. Ortiz, and R. Phillips, Philos.
Mag. A 73 (6) (1996) p. 1529.
20. E.B. Tadmor, R. Phillips, and M. Ortiz,
Langmuir 12 (19) (1996) p. 4529.
21. V.B. Shenoy, R. Miller, E.B. Tadmor, R. Phillips,
and M. Ortiz, Phys. Rev. Lett. 80 (4) (1998) p. 742.
22. R. Miller, E.B. Tadmor, R. Phillips, and M.
Ortiz, Model. Simul. Mater. Sci. Eng. 6 (5) (1998)
p. 607.
43. G. Wang, A. Strachan, T. Cagin, and W.A.
Goddard III, Mater. Sci. Eng., A (2001) in press.
44. A. Strachan, G. Wang, T. Cagin, and W.A.
Goddard III (private communication, 2000).
45. M.I. Baskes, R.G. Hoagland, and T. Tsuji,
Model. Simul. Mater. Sci. Eng. 6 (1) (1998) p. 9.
46. M. Rhee, H.M. Zbib, J.P. Hirth, H. Huang,
and T. Diaz de la Rubia, Model. Simul. Mater. Sci.
Eng. 6 (4) (1998) p. 467.
47. L.P. Kubin, B. Devincre, and M. Tang,
J. Comput.-Aided Mater. Des. 5 (1998) p. 31.
48. H.C. Huang, N. Ghoniem, T. Diaz de la Rubia,
M. Rhee, H. Zbib, and J. Hirth, Trans. ASME
J. Eng. Mater. Technol. 121 (2) (1999) p. 143.
49. V.B. Shenoy, R.V. Kukta, and R. Phillips,
Phys. Rev. Lett. 84 (7) (2000) p. 1491.
50. H.M. Zbib, T. Diaz de la Rubia, M. Rhee,
and J.P. Hirth, J. Nucl. Mater. 276 (2000) p. 154.
51. A.M. Cuitiño, M. Koslowski, M. Ortiz, and
L. Stainier, “APhase-Field Theory of Dislocation
Dynamics, Strain Hardening and Hysteresis in
Ductile Single Crystals at Low Temperatures,”
Philos. Mag. A, submitted for publication, 2000.
52. M. Ortiz and E.P. Popov, Proc. R. Soc. London,
Ser. A 379 (1982) p. 439.
Concluding Remarks
The emerging synergism between the
atomistic and continuum views of mate-
rial behavior demonstrates how the link-
ing of these perspectives often results in
more theoretical power than either offers
alone. In closing, it is worth noting how
the present emphasis on multiscale mod-
eling of materials has brought together
disciplinary groups which have tradi-
tionally operated largely in isolation of
each other, including chemists, applied
physicists, materials scientists, applied
mathematicians, computer scientists, and
continuum mechanicians.
23. R. Miller, M. Ortiz, R. Phillips, V. Shenoy,
and E.B. Tadmor, Eng. Fracture Mech. 61 (3–4)
(1998) p. 427.
24. D. Rodney and R. Phillips, Phys. Rev. Lett.
82 (8) (1999) p. 1704.
53. S.R. Bodner and A. Lindenfeld, Euro.
J.Mech., A/Solids 14 (3) (1995) p. 333.
25. V.B. Shenoy, R. Miller, E.B. Tadmor, D.
Rodney, R. Phillips, and M. Ortiz, J. Mech. Phys.
Solids 47 (3) (1999) p. 611.
26. E.B. Tadmor, R. Miller, R. Phillips, and M.
Ortiz, J. Mater. Res. 14 (6) (1999) p. 2233.
27. V.B. Shenoy, R. Phillips, and E.B. Tadmor,
J. Mech. Phys. Solids 48 (4) (2000) p. 649.
28. G.S. Smith, E.B. Tadmor, and E. Kaxiras,
Phys. Rev. Lett. 84 (2000) p. 1260.
29. J. Knap and M. Ortiz, “An Analysis of the
Quasi-Continuum Method,” J. Mech. Phys.
Solids (2001) in press.
30. V. Shenoy, V. Shenoy, and R. Phillips, in
Multiscale Modeling of Materials, edited by V.V.
54. J.P. Sethna, K. Dahmen, S. Kartha, J.A.
Krumhansl, B.W. Roberts, and J.D. Shore, Phys.
Rev. Lett. 70 (1993) p. 3347.
55. K. Dahmen, S. Kartha, J.A. Krumhansl,
B.W. Roberts, J.P. Sethna, and J.D. Shore, J. Appl.
Phys. 75 (1994) p. 5946.
56. W. Xu and J.A. Moriarty, Phys. Rev. B 54 (10)
(1996) p. 6941.
57. S. Ismail-Beigi and T.A. Arias, Phys. Rev.
Lett. 84 (7) (2000) p. 1499.
Acknowledgments
The support of the U.S. Department of
Energy through California Institute of
Technology’s ASCI/ASAP Center for the
Simulation of the Dynamic Response of
Materials is gratefully acknowledged.
References
1. T.E. Mason and A.D. Taylor, guest editors,
“Neutron Scattering in Materials Research,”
MRS Bull. 24 (12) (1999) pp. 14–47.
58. D. Olmsted and R. Phillips (unpublished).
59. M.S. Duesbery and W. Xu, Scripta Mater. 39
2. E. Wasserman, L. Stixrude, and R.E. Cohen,
Phys. Rev. B: Condens. Matter 53 (13) (1996) p. 8296.
(3) (1998) p. 283.
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