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Dynamic Fracture of Silicon: Concurrent Simulation of Quantum Electrons, Classical Atoms, and the Continuum Solid

Published online by Cambridge University Press:  31 January 2011

Farid F. Abraham ,
Noam Bernstein ,
Jeremy Q. Broughton  and
Daryl Hess
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Extract

Our understanding of materials phenomena is based on a hierarchy of physical descriptions spanning the space-time regimes of electrons, atoms, and matter and given by the theories of quantum mechanics, statistical mechanics, and continuum mechanics. The pioneering work of Clementi and co-workers provides a lucid example of the traditional approach to incorporating multiscale phenomena associated with these three mechanics. Using quantum mechanics, they evaluated the interactions of several water molecules. From this data base, they created an empirical potential for use in atomistic mechanics and evaluated the viscosity of water. From this computed viscosity, they performed a fluid-dynamics simulation to predict the tidal circulation in Buzzard's Bay. This is a powerful example of the sequential coupling of length and time scales: a series of calculations is used as input to the next rung up the length/time-scale ladder.

Type
Research Article
Information
MRS Bulletin , Volume 25 , Issue 5: Theory and Simulation of Fracture , May 2000 , pp. 27 - 32
Copyright
Copyright © Materials Research Society 2000

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References

1.Clementi, E., Philos. Trans. R. Soc. London, Ser. A 326 (1988) p. 445.Google Scholar
2.Freund, L.B., Dynamic Fracture Mechanics (Cambridge University Press, New York, 1990).CrossRefGoogle Scholar
3.Abraham, F.F., Brodbeck, D., Rafey, R.A., and Rudge, W.E., Phys. Rev. Lett. 73 (1994) p. 272; F.F. Abraham, D. Schneider, B. Land, D. Lifka, J. Skovira, J. Gerner, and M. Rosenkrantz, J. Mech. Phys. Solids 45 (1997) p. 1461.CrossRefGoogle Scholar
4.Nakano, A., Kalia, R.K., and Vashishta, P., Phys. Rev. Lett. 75 (1995) p. 3138; A. Omeltchenko, J. Yu, R.K. Kalia, and P. Vashishta, Phys. Rev. Lett. 78 (1997) p. 2148.CrossRefGoogle Scholar
5.Abraham, F.F., Broughton, J.Q., Bernstein, N., and Kaxiras, E., Comput. Phys. 12 (1998) p. 538; Europhys. Lett. 44 (1998) p. 783.CrossRefGoogle Scholar
6.Kohlhoff, S., Gumbsch, P., and Fischmeister, H.F., Philos. Mag. A 64 (4) (1991) p. 851.CrossRefGoogle Scholar
7.Hoover, W., De Groot, A., and Hoover, C., Comput. Phys. 6 (1992) p. 155.CrossRefGoogle Scholar
8.Rafii-Tabar, H., Hua, L., and Cross, M., J. Phys.: Condens. Matter 10 (1998) p. 2375.Google Scholar
9.Shenoy, V., Miller, R., Tadmor, E., and Phillips, R., Phys. Rev. Lett. 80 (1998) p. 742.CrossRefGoogle Scholar
10.Capaz, R., Cho, K., and Joannopoulos, J., Phys. Rev. Lett. 75 (1995) p. 1811.CrossRefGoogle Scholar
11.Vanduijnen, P. and Devries, A., Int. J. Quantum Chem. 60 (1996) p. 1111.3.0.CO;2-2>CrossRefGoogle Scholar
12.Hughes, T., The Finite Element Method (Prentice-Hall, Englewood Cliffs, NJ, 1987).Google Scholar
13.Stillinger, F.H. and Weber, T.A., Phys. Rev. B 31 (1985) p. 5262.CrossRefGoogle Scholar
14.Bazant, M.Z., Kaxiras, E., and Justo, J.F., Phys. Rev. B 56 (1997) p. 8542; J.F. Justo, M.Z. Bazant, E. Kaxiras, V.V. Bulatov, and S. Yip, Phys. Rev. B 58 (1998) p. 2539.CrossRefGoogle Scholar
15.Bernstein, N. and Kaxiras, E., Phys. Rev. B 56 (1997) p. 10488.CrossRefGoogle Scholar
16.Bernstein, N., in preparation.Google Scholar
17.Nicholson, D.M.C. and Zhang, X.-G., Phys. Rev. B 56 (1997) p. 12805.CrossRefGoogle Scholar
18.Press, W.H., Teukolsky, S.A., Vetterling, W.T., and Flannery, B.P., Numerical Recipes in C: The Art of Scientific Computing, 2nd ed. (Cambridge University Press, Cambridge, UK, 1992).Google Scholar
19.Hauch, J.A., Holland, D., Marder, M.P., and Swinney, H.L., Phys. Rev. Lett. 82 (1999) p. 3823.CrossRefGoogle Scholar
20.Bernstein, N. and Hess, D.W., in preparation.Google Scholar