Hostname: page-component-586b7cd67f-t8hqh Total loading time: 0 Render date: 2024-11-26T15:12:30.009Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  31 January 2011

Ronald E. Miller  and
Ellad B. Tadmor
Get access

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.

Type
Research Article
Information
MRS Bulletin , Volume 32 , Issue 11: Multiscale Modeling in Advanced Materials Research , November 2007 , pp. 920 - 926
Copyright
Copyright © Materials Research Society 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Saraev, D., Miller, R.E., Acta Mater. 54 (1), 33 (2006).CrossRefGoogle Scholar
2.Tadmor, E.B., Miller, R.E., Quasicontinuum Method Web site, www.qcmethod.com (accessed August 2007).Google Scholar
3.Kohlhoff, S., Gumbsch, P., Fischmeister, H.F., Philos. Mag. A 64 (4), 851 (1991).CrossRefGoogle Scholar
4.Tadmor, E.B., Ortiz, M., Phillips, R., Philos. Mag. A 73 (6), 1529 (1996).CrossRefGoogle Scholar
5.Tadmor, E.B., Phillips, R., Ortiz, M., Langmuir 12 (19), 4529 (1996).CrossRefGoogle Scholar
6.Insepov, Z., Sosnowski, M., Yamada, I., Nucl. Instrum. Methods Phys. Res. B 127, 269 (1997).CrossRefGoogle Scholar
7.Shenoy, V.B., Miller, R., Tadmor, E.B., Phillips, R., Ortiz, M., Phys. Rev. Lett. 80 (4), 742 (1998).CrossRefGoogle Scholar
8.Shenoy, V.B., Miller, R., Tadmor, E.B., Rodney, D., Phillips, R., Ortiz, M., J. Mech. Phys. Sol. 47, 611 (1999).CrossRefGoogle Scholar
9.Rudd, R.E., Broughton, J.Q., Phys. Rev. B 58 (10), R5893 (1998).CrossRefGoogle Scholar
10.Abraham, F.F., Bernstein, N., Broughton, J.Q., Hess, D., MRS Bull. 25 (5), 27 (2000).CrossRefGoogle Scholar
11.Rudd, R.E., Broughton, J.Q., Phys. Status Solidi B 217, 251 (2000).3.0.CO;2-A>CrossRefGoogle Scholar
12.Lidorikis, E., Bachlechner, M.E., Kalia, R.K., Nakano, A., Vashishta, P., Voyiadjis, G.Z., Phys. Rev. Lett. 87 (8), 086104/1–4 (2001).CrossRefGoogle Scholar
13.E, W., Huang, Z., Phys. Rev. Lett. 87 (13), 135501–1 (2001).CrossRefGoogle Scholar
14.Shilkrot, L.E., Miller, R.E., Curtin, W.A., Phys. Rev. Lett. 89 (2), 025501 (2002).CrossRefGoogle Scholar
15.Wagner, G.J., Liu, W.K., J. Comput. Phys. 190, 249 (2003).CrossRefGoogle Scholar
16.Xiao, S.P., Belytschko, T., Comput. Methods Appl. Mech. Eng. 193, 1645 (2004).CrossRefGoogle Scholar
17.Datta, D.K., Picu, R. Catalin, Shephard, M.S., Int. J. Multiscale Computational Eng. 2 (3), 71 (2004).CrossRefGoogle Scholar
18.Fish, J., Chen, W., Comput. Methods Appl. Mech. Eng. 193, 1693 (2004).CrossRefGoogle Scholar
19.Shilkrot, L.E., Miller, R.E., Curtin, W.A., J. Mech. Phys. Sol. 52 (4), 755 (2004).CrossRefGoogle Scholar
20.Wagner, G.J., Karpov, E.G., Liu, W.K., Comput. Methods Appl. Mech. Eng. 193, 1579 (2004).CrossRefGoogle Scholar
21.Rudd, R.E., Broughton, J.Q., Phys. Rev. B 72 (14), 144104 (2005).CrossRefGoogle Scholar
22.Luan, B.Q., Hyun, S., Molinari, J.F., Bernstein, N., Robbins, M.O., Phys. Rev. E 74, 046710–1 (2007).CrossRefGoogle Scholar
23.Zhou, S.J., Carlsson, A.E., Thomson, R., Phys. Rev. B 47 (13), 7710 (1993).CrossRefGoogle Scholar
24.Woodward, C., Rao, S.I., Phys. Rev. Lett. 88 (21), 216402/1–4 (2002).CrossRefGoogle Scholar
25.Shen, S., Atluri, S.N., Comput. Model. Eng. Sci. 5, 235 (2004).Google Scholar
26.Curtin, W.A., Miller, R.E., Model. Simul. Mater. Sci. Eng. 11 (3), R33 (2003).CrossRefGoogle Scholar
27.Miller, R.E., Int. J. Multiscale Comput. Eng. 1 (1), 57 (2003).CrossRefGoogle Scholar
28.Miller, R.E., Tadmor, E.B., J. Comput. Aided Mater. Des. 9, 203 (2002).CrossRefGoogle Scholar
29.Liu, W.K., Karpov, E.G., Zhang, S., Park, H.S., Comput. Methods Appl. Mech. Eng. 193, 1529 (2004).CrossRefGoogle Scholar
30.Park, H.S., Liu, W.K., Comput. Methods Appl. Mech. Eng. 193, 1733 (2004).CrossRefGoogle Scholar
31.Lu, G., Kaxiras, E., Handbook of Theoretical and Computational Nanotechnology (American Scientific Publishers, Stevenson Ranch, Calif., 2005, vol. 4) p. 22.Google Scholar
32.E, W., Engquist, B., Li, X., Ren, W., Vanden-Eijnden, E., Commun. Comput. Phys. 2 (3), 367 (2007).Google Scholar
33.Gao, H., Klein, P., J. Mech. Phys. Sol. 46 (2), 187 (1998).CrossRefGoogle Scholar
34.Klein, P., Gao, H., Eng. Fracture Mech. 61, 21 (1998).CrossRefGoogle Scholar
35.Johnson, H.T., Phillips, R., Freund, L.B., “Electronic Structure Boundary Value Problems without All of the Atoms,” in Mater. Res. Soc. Symp. Proc. 538 Bulatov, V.V., de la Rubia, T. Diaz, Phillips, R., Kaxiras, E., Ghoniem, N., eds. (Materials Research Society, Warrendale, PA, 1999) p. 479.Google Scholar
36.Zhang, P., Klein, P.A., Huang, Y., Gao, H., Wu, P.D., Comput. Model. Eng. Sci. 3 (2), 263 (2002).Google Scholar
37.Zhang, P., Huang, Y., Gao, H., Hwang, K.C., J. Appl. Mech. 69, 454 (2002).CrossRefGoogle Scholar
38.Zhang, P., Huang, Y., Geubelle, P.H., Klein, P.A., Hwang, K.C., Int. J. Sol. Struct. 39, 3893 (2002).CrossRefGoogle Scholar
39.Van Vliet, K.J., Li, J., Zhu, T., Yip, S., Suresh, S., Phys. Rev. B 67, 104105 (2003).CrossRefGoogle Scholar
40.Born, M., Huang, K., Dynamical Theory of Crystal Lattices (Clarendon, Oxford, 1954).Google Scholar
41.Tadmor, E.B., Smith, G.S., Bernstein, N., Kaxiras, E., Phys. Rev. B 59 (1), 235 (1999).CrossRefGoogle Scholar
42.Smith, G.S., Tadmor, E.B., Kaxiras, E., Phys. Rev. Lett. 84 (6), 1260 (2000).CrossRefGoogle Scholar
43.Pitteri, M., Arch. Rational Mech. Anal. 88, 25 (1985).CrossRefGoogle Scholar
44.Zanzotto, G., Atti Accad. Naz. Lincei, Rend. Fis. 82, 725742, 743756 (1988).Google Scholar
45.Zanzotto, G., Arch. Rational Mech. Anal. 121, 1 (1992).CrossRefGoogle Scholar
46.Dobson, M., Elliott, R.S., Luskin, M., Tadmor, E.B., Sci. Model. Simul. (2008) in press.Google Scholar
47.E, W., Lu, J., Yang, J.Z., Phys. Rev. B 74 (21), 214115/1–12 (2006).CrossRefGoogle Scholar
48.Shimokawa, T., Mortensen, J.J., Schitz, J., Jacobsen, K.W., Phys. Rev. B 69, 214104/1–10 (2004).CrossRefGoogle Scholar
49.Knap, J., Ortiz, M., J. Mech. Phys. Sol. 49, 1899 (2001).CrossRefGoogle Scholar
50.Knap, J., Ortiz, M., Phys. Rev. Lett. 90, 226102 (2003).CrossRefGoogle Scholar
51.Prudhomme, S., Bauman, P., Oden, J.T., Int. J. Multiscale Comp. Eng. 4, 647 (2007).CrossRefGoogle Scholar
52. Marcel Arndt and Mitchell Luskin, “Error estimation and atomistic-continuum adaptivity for the quasicontinuum approximation of a Frenkel-Kontorova model,” SIAM J. Multiscale Model. & Simul. (2007) in press.CrossRefGoogle Scholar
53.Miller, R., Tadmor, E.BPhillips, R.Ortiz, M., Model. Simul. Mater. Sci. Eng. 6, 607 (1998).CrossRefGoogle Scholar
54.Pillai, A.R.Miller, R.E. “Crack Behaviour at Bi-Crystal Interfaces: A Mixed Atomistic and Continuum Approach,” in Mater. Res. Soc. Symp. Proc. 653, Kubin, L.P, Selinger, R.L., Bassani, J.L., Cho, K., Eds. (Materials Research Society, Warrendale, PA, 2001) Z2.9.1.Google Scholar
55.Hai, S., Tadmor, E.B., Acta Mater. 51 (1), 117 (2003).CrossRefGoogle Scholar
56.Sansoz, F., Molinari, J.F., Scripta Mater. 50, 1283 (2004).CrossRefGoogle Scholar
57.Sansoz, F., Molinari, J.F., Acta Mater. 53, 1931 (2005).CrossRefGoogle Scholar
58.Tadmor, E.B., Miller, R., Phillips, R., Ortiz, M., J. Mater. Res. 14 (6), 2233 (1999).CrossRefGoogle Scholar
59.Miller, R.E., Shilkrot, L.E., Curtin, W.A., Acta Mater. 52 (2), 271 (2003).CrossRefGoogle Scholar
60.Fago, M., Hayes, R.L., Carter, E.A., Ortiz, M., Phys. Rev. B 70 (10), 100102 (2004).CrossRefGoogle Scholar
61.Smith, G.S., Tadmor, E.B., Bernstein, N., Kaxiras, E., Acta Mater. 49 (19), 4089 (2001).CrossRefGoogle Scholar
62.Tadmor, E.B., Waghmare, U.V., Smith, G.S., Kaxiras, E., Acta Mater. 50, 2989 (2002).CrossRefGoogle Scholar
63.Qian, D., Wagner, G.J., Liu, W.K., Comput. Methods Appl. Mech. Eng. 193, 1603 (2004).CrossRefGoogle Scholar
64.Lin, P., Math. Comput. 72 (242), 657 (2003).CrossRefGoogle Scholar
65.Ming, W.E.P., J. Comput. Math. 22, 210 (2004).Google Scholar
66.Ming, W.E.P., Frontiers and Prospects of Contemporary Applied Mathematics, Li, T., Zhang, P., Eds., (Higher Education Press, World Scientific, Singapore, 2005, vol. 18).Google Scholar
67.Blanc, X., Bris, C. Le, Legoll, F., ESAIM: M2AN 39, 797 (2005).CrossRefGoogle Scholar
68.Blanc, X., Bris, C. Le, Lions, P.L., ESAIM: M2AN 41 391 (2007).CrossRefGoogle Scholar
69.Lin, P., SIAM J. Numer. Anal. 45 (1), 313 (2007).CrossRefGoogle Scholar
70.Dobson, M., Luskin, M., ESAIM: M2AN (2007) in press.Google Scholar
71.Hughes, T.J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis (Prentice-Hall, Englewood Cliffs, N.J., 1987).Google Scholar
72.Zienkiewicz, O.C., Taylor, R.L., The Finite Element Method (McGraw-Hill, London, vol. 1, ed. 4, 1989).Google Scholar
73.Reddy, J.N., An Introduction to the Finite Element Method (McGraw-Hill, New York, ed. 2, 1993).Google Scholar
74.Bažant, Z.P., Comp. Methods Appl. Mech. Eng. 16, 91 (1978).CrossRefGoogle Scholar
75.Mullen, R., Belytschko, T., Int. J. Num. Methods Eng. 18, 11 (1982).CrossRefGoogle Scholar
76.Adelman, S.A., Doll, J.D., J. Chem. Phys. 61 (10), 4242 (1974).CrossRefGoogle Scholar
77.Doll, J.D., Myers, L.E., J. Chem. Phys. 63 (11), 4908 (1975).CrossRefGoogle Scholar
78.Cai, W., de Koning, M., Bulatov, V.V., Yip, S., Phys. Rev. Lett. 85 (15), 3213 (2000).CrossRefGoogle Scholar
79.Hoover, W.G., Molecular Dynamics (Springer, Berlin, 1986).Google Scholar
80.Allen, M.P., Tildesley, D.J., Computer Simulation of Liquids (Clarendon Press, Oxford, 1987).Google Scholar
81.Frenkel, D., Smit, B., Understanding Molecular Simulation: From Algorithms to Applications (Academic Press, San Diego, ed. 2, 2002).Google Scholar
82.Holian, B.L., Voter, A.F., Ravelo, R., Phys. Rev. E 52 (3), 2338 (1995).CrossRefGoogle Scholar
83.Dupuy, L.M., Tadmor, E.B., Miller, R.E., Phillips, R., Phys. Rev. Lett. 95, 060202 (2005).CrossRefGoogle Scholar
84.Qu, S., Shastry, V., Curtin, W.A., Miller, R.E., Model. Simul. Mater. Sci. Eng. 13 (7), 1101 (2005).CrossRefGoogle Scholar
85.Holian, B.L., Ravelo, R., Phys. Rev. B 51 (17), 11275 (1995).CrossRefGoogle Scholar
86.Holland, D., Marder, M., Adv. Mater. 11, 793 (1999).3.0.CO;2-B>CrossRefGoogle Scholar
87.Shiari, B., Miller, R.E., Curtin, W.A., ASME J. Eng. Mater. Technol.–Trans. ASME 127 (4), 358 (2005).CrossRefGoogle Scholar
88.Shiari, B., Miller, R.E., Klug, D.D., J. Mech. Phys. Solids (2007) in press.Google Scholar
89.Finnis, M.W., Agnew, P., Foreman, A.J.E., Phys. Rev. B 44 (2), 567 (1991).CrossRefGoogle Scholar
90.Choly, N., Lu, G., E, W., Kaxiras, E., Phys. Rev. B 71 (9), 094101 (2005).CrossRefGoogle Scholar
91.Lu, G., Tadmor, E.B., Kaxiras, E., Phys. Rev. B 73 (2) 024108 (2006).CrossRefGoogle Scholar