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Hybrid Continuum Mechanics and Atomistic Methods for Simulating Materials Deformation and Failure

Abstract
Abstract

Many aspects of materials deformation and failure are controlled by atomic-scale phenomena that can be explored using molecular statics and molecular dynamics simulations. However, many of these phenomena involve processes on multiple length scales with the result that full molecular statics/molecular dynamics simulations of the entire system are too large to be tractable. In this review, we discuss hybrid models that perform molecular statics/molecular dynamics simulations “without all the atoms,” aimed at retaining atomistic detail at a fraction of the computational cost. These methods couple a fully atomistic model in critical regions to regions described by less-expensive continuum methods where they can provide an adequate representation of the important physics. We give an overview of the challenges such models present, with a focus on recent work to address issues of dynamics and finite (non-zero) temperature.

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1. D. Saraev , R.E. Miller , Acta Mater. 54 (1), 33 (2006).

3. S. Kohlhoff , P. Gumbsch , H.F. Fischmeister , Philos. Mag. A 64 (4), 851 (1991).

4. E.B. Tadmor , M. Ortiz , R. Phillips , Philos. Mag. A 73 (6), 1529 (1996).

5. E.B. Tadmor , R. Phillips , M. Ortiz , Langmuir 12 (19), 4529 (1996).

7. V.B. Shenoy , R. Miller , E.B. Tadmor , R. Phillips , M. Ortiz , Phys. Rev. Lett. 80 (4), 742 (1998).

8. V.B. Shenoy , R. Miller , E.B. Tadmor , D. Rodney , R. Phillips , M. Ortiz , J. Mech. Phys. Sol. 47, 611 (1999).

9. R.E. Rudd , J.Q. Broughton , Phys. Rev. B 58 (10), R5893 (1998).

10. F.F. Abraham , N. Bernstein , J.Q. Broughton , D. Hess , MRS Bull. 25 (5), 27 (2000).

11. R.E. Rudd , J.Q. Broughton , Phys. Status Solidi B 217, 251 (2000).

12. E. Lidorikis , M.E. Bachlechner , R.K. Kalia , A. Nakano , P. Vashishta , G.Z. Voyiadjis , Phys. Rev. Lett. 87 (8), 086104/1–4 (2001).

13. W. E , Z. Huang , Phys. Rev. Lett. 87 (13), 135501–1 (2001).

14. L.E. Shilkrot , R.E. Miller , W.A. Curtin , Phys. Rev. Lett. 89 (2), 025501 (2002).

15. G.J. Wagner , W.K. Liu , J. Comput. Phys. 190, 249 (2003).

16. S.P. Xiao , T. Belytschko , Comput. Methods Appl. Mech. Eng. 193, 1645 (2004).

17. D.K. Datta , R. Catalin Picu , M.S. Shephard , Int. J. Multiscale Computational Eng. 2 (3), 71 (2004).

18. J. Fish , W. Chen , Comput. Methods Appl. Mech. Eng. 193, 1693 (2004).

19. L.E. Shilkrot , R.E. Miller , W.A. Curtin , J. Mech. Phys. Sol. 52 (4), 755 (2004).

20. G.J. Wagner , E.G. Karpov , W.K. Liu , Comput. Methods Appl. Mech. Eng. 193, 1579 (2004).

21. R.E. Rudd , J.Q. Broughton , Phys. Rev. B 72 (14), 144104 (2005).

22. B.Q. Luan , S. Hyun , J.F. Molinari , N. Bernstein , M.O. Robbins , Phys. Rev. E 74, 046710–1 (2007).

23. S.J. Zhou , A.E. Carlsson , R. Thomson , Phys. Rev. B 47 (13), 7710 (1993).

24. C. Woodward , S.I. Rao , Phys. Rev. Lett. 88 (21), 216402/1–4 (2002).

26. W.A. Curtin , R.E. Miller , Model. Simul. Mater. Sci. Eng. 11 (3), R33 (2003).

27. R.E. Miller , Int. J. Multiscale Comput. Eng. 1 (1), 57 (2003).

28. R.E. Miller , E.B. Tadmor , J. Comput. Aided Mater. Des. 9, 203 (2002).

29. W.K. Liu , E.G. Karpov , S. Zhang , H.S. Park , Comput. Methods Appl. Mech. Eng. 193, 1529 (2004).

30. H.S. Park , W.K. Liu , Comput. Methods Appl. Mech. Eng. 193, 1733 (2004).

33. H. Gao , P. Klein , J. Mech. Phys. Sol. 46 (2), 187 (1998).

34. P. Klein , H. Gao , Eng. Fracture Mech. 61, 21 (1998).

35. H.T. Johnson , R. Phillips , L.B. Freund , “Electronic Structure Boundary Value Problems without All of the Atoms,” in Mater. Res. Soc. Symp. Proc. 538 V.V. Bulatov , T. Diaz de la Rubia , R. Phillips , E. Kaxiras , N. Ghoniem , eds. (Materials Research Society, Warrendale, PA, 1999) p. 479.

37. P. Zhang , Y. Huang , H. Gao , K.C. Hwang , J. Appl. Mech. 69, 454 (2002).

38. P. Zhang , Y. Huang , P.H. Geubelle , P.A. Klein , K.C. Hwang , Int. J. Sol. Struct. 39, 3893 (2002).

39. K.J. Van Vliet , J. Li , T. Zhu , S. Yip , S. Suresh , Phys. Rev. B 67, 104105 (2003).

41. E.B. Tadmor , G.S. Smith , N. Bernstein , E. Kaxiras , Phys. Rev. B 59 (1), 235 (1999).

42. G.S. Smith , E.B. Tadmor , E. Kaxiras , Phys. Rev. Lett. 84 (6), 1260 (2000).

43. M. Pitteri , Arch. Rational Mech. Anal. 88, 25 (1985).

45. G. Zanzotto , Arch. Rational Mech. Anal. 121, 1 (1992).

47. W. E , J. Lu , J.Z. Yang , Phys. Rev. B 74 (21), 214115/1–12 (2006).

48. T. Shimokawa , J.J. Mortensen , J. Schitz , K.W. Jacobsen , Phys. Rev. B 69, 214104/1–10 (2004).

49. J. Knap , M. Ortiz , J. Mech. Phys. Sol. 49, 1899 (2001).

50. J. Knap , M. Ortiz , Phys. Rev. Lett. 90, 226102 (2003).

51. S. Prudhomme , P. Bauman , J.T. Oden , Int. J. Multiscale Comp. Eng. 4, 647 (2007).

53. R. Miller , E.B Tadmor R. Phillips M. Ortiz , Model. Simul. Mater. Sci. Eng. 6, 607 (1998).

55. S. Hai , E.B. Tadmor , Acta Mater. 51 (1), 117 (2003).

56. F. Sansoz , J.F. Molinari , Scripta Mater. 50, 1283 (2004).

57. F. Sansoz , J.F. Molinari , Acta Mater. 53, 1931 (2005).

59. R.E. Miller , L.E. Shilkrot , W.A. Curtin , Acta Mater. 52 (2), 271 (2003).

60. M. Fago , R.L. Hayes , E.A. Carter , M. Ortiz , Phys. Rev. B 70 (10), 100102 (2004).

61. G.S. Smith , E.B. Tadmor , N. Bernstein , E. Kaxiras , Acta Mater. 49 (19), 4089 (2001).

62. E.B. Tadmor , U.V. Waghmare , G.S. Smith , E. Kaxiras , Acta Mater. 50, 2989 (2002).

63. D. Qian , G.J. Wagner , W.K. Liu , Comput. Methods Appl. Mech. Eng. 193, 1603 (2004).

64. P. Lin , Math. Comput. 72 (242), 657 (2003).

67. X. Blanc , C. Le Bris , F. Legoll , ESAIM: M2AN 39, 797 (2005).

68. X. Blanc , C. Le Bris , P.L. Lions , ESAIM: M2AN 41 391 (2007).

69. P. Lin , SIAM J. Numer. Anal. 45 (1), 313 (2007).

74. Z.P. Bažant , Comp. Methods Appl. Mech. Eng. 16, 91 (1978).

75. R. Mullen , T. Belytschko , Int. J. Num. Methods Eng. 18, 11 (1982).

76. S.A. Adelman , J.D. Doll , J. Chem. Phys. 61 (10), 4242 (1974).

77. J.D. Doll , L.E. Myers , J. Chem. Phys. 63 (11), 4908 (1975).

78. W. Cai , M. de Koning , V.V. Bulatov , S. Yip , Phys. Rev. Lett. 85 (15), 3213 (2000).

81. D. Frenkel , B. Smit , Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, San Diego, ed. 2, 2002).

82. B.L. Holian , A.F. Voter , R. Ravelo , Phys. Rev. E 52 (3), 2338 (1995).

83. L.M. Dupuy , E.B. Tadmor , R.E. Miller , R. Phillips , Phys. Rev. Lett. 95, 060202 (2005).

84. S. Qu , V. Shastry , W.A. Curtin , R.E. Miller , Model. Simul. Mater. Sci. Eng. 13 (7), 1101 (2005).

85. B.L. Holian , R. Ravelo , Phys. Rev. B 51 (17), 11275 (1995).

86. D. Holland , M. Marder , Adv. Mater. 11, 793 (1999).

87. B. Shiari , R.E. Miller , W.A. Curtin , ASME J. Eng. Mater. Technol.–Trans. ASME 127 (4), 358 (2005).

89. M.W. Finnis , P. Agnew , A.J.E. Foreman , Phys. Rev. B 44 (2), 567 (1991).

90. N. Choly , G. Lu , W. E , E. Kaxiras , Phys. Rev. B 71 (9), 094101 (2005).

91. G. Lu , E.B. Tadmor , E. Kaxiras , Phys. Rev. B 73 (2) 024108 (2006).

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MRS Bulletin
  • ISSN: 0883-7694
  • EISSN: 1938-1425
  • URL: /core/journals/mrs-bulletin
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