An adaptive finite element approach to atomic-scale mechanics - The quasicontinuum method

Journal of the Mechanics and Physics of Solids

Volumn 47, Issue 3, 1999, Pages 611-642

  Shenoy, V B ^a   Miller, R ^a   Tadmor, E B ^b   Rodney, D ^a   Phillips, R ^a   Ortiz, M ^c  

^a Brown University   (United States)

^b HARVARD UNIVERSITY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

A. Dislocations; A. Grain boundaries; B. Constitutive behaviour; C. Finite elements

Indexed keywords

COMPUTER SIMULATION; CRYSTALLOGRAPHY; DISLOCATIONS (CRYSTALS); FINITE ELEMENT METHOD; GRAIN BOUNDARIES; MATHEMATICAL MODELS; SINGLE CRYSTALS;

ATOMIC-SCALE MECHANICS; QUASICONTINUUM METHOD;

CONTINUUM MECHANICS;

EID: 0033100627     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(98)00051-9     Document Type: Article

References (26)

1. Ackland, G.J., Tichy, G., Vitek, V., Finnis, M.W., 1987. Simple N-body potentials for the noble-metals and nickel. Philosophical Magazine A56, 735-756.
2. Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, 55-129.
3. Belytschko, T., Tabbara, M., 1993. H-adaptive finite-element methods for dynamic problems, with emphasis on localization. International Journal of Numerical Methods in Engineering 36, 4245-4265.
4. Chadwick, P., 1976. Continuum Mechanics. John Wiley and Sons, New York.
5. Christian, J. W. (1983) Some surprising features of the plastic deformation of body-centered cubic metals and alloys. Metallurgical Transactions A14, 1237-1256.
6. Dahmen, U., Hetherington, C.J., Okeefe, M.A., Westmacott, K.H., Mills, M.J., Daw, M.J., Vitek, V., 1990. Atomic-structure of a sigma-99 grain boundary in aluminum - a comparison between atomic-resolution observation and pair-potential and embedded-atom simulations. Philosophical magazine Letters 62, 327-335.
7. Daw, M.S., Baskes, M.I., 1983. Semiempirical, quantum-mechanical calculations of hydrogen embrittlement in metals. Physical Review Letters 50, 1285-1288.
8. Dennis, J.E. Jr., Schnabel, R.B., 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs.
9. Ercolessi, F., Adams, J., 1993. Interatomic potentials from 1st-principles calculations - the force-matching method. Europhysics Letters 26, 583-588.
10. Ericksen, J.L., 1984. The Cauchy-Born hypothesis for crystals. In Phase Transformations and Material Instabilities in Solids, ed. M. Gurtin, pp. 61-77. Academic Press.
11. Gerberich, W.W., Nelson, J.C., Lilleodden, E.T., Anderson, P., Wyrobek, J.T., 1966. Indentation induced dislocation - the initial yield-point. Acta Materiala 44, 3585-3598.
12. Hirth, J.P., Lothe, J., 1968. Theory of Dislocations. McGraw-Hill, New York.
13. Hull, D., Bacon, D.J., 1992. Introduction to Dislocations. Pergamon Press, Oxford.
14. King, A.H., Smith, D A., 1980. The effects on grain boundary processes of steps in the boundary plane associated with the core of grain boundary dislocations. Acta Crystallographica A36, 335-343.
15. Kohlhoff, S., Gumbsch, P., Fischmeister, H.F., 1991. Crack-propagation in bcc crystal studied with a combined finite-element and atomistic model. Philosophical Magazine A64, 851-878.
16. Okabe, A., Boots, B., Sugihara, K., 1992. Spatial Tessellations. Wiley and Sons, New York.
17. Papadrakakis, M., Ghionis, P., 1986. Conjugate-gradient algorithms in nonlinear structural-analysis problems. Computer Methods in Applied Mechanics Engineering 59, 11-27.
18. Peierls, R.E., 1940. The size of a dislocation. Proceedings of the Physical Society of London 52, 34-37.
19. Shenoy, V.B., Phillips, R., 1997. Finite-sized atomistic simulations of screw dislocations. Philosophical Magazine A76, 367-385.
20. Sloan, S.W., 1993. A fast algorithm for generating constrained Delaunay triangulations. Computers and Structures 47, 441-450.
21. Tadmor, E.B., 1996. The quasicontinuum method. Ph.D. Thesis, Brown University.
22. Tadmor, E.B., Ortiz, M., Phillips, R., 1996. Quasicontinuum analysis of defects in solids. Philosophical Magazine A73, 1529-1563.
23. Tadmor, E.B., Miller, R., Phillips, R., Ortiz, M., 1997. Quasicontinuum analysis of nanoindentation. To be submitted to Acta Materiala.
24. Thomson, R., Zhou, S.J., Carlsson, A.E., Tewary, V.K., 1992. Lattice imperfections studied by use of lattice green-functions. Physical Review B, 46, 10,613-10,622.
25. Xu, X.-P., Argon, A.S., Ortiz, M., 1995. Nucleation of dislocations from crack tips under mixed-modes of loading - implications for brittle against ductile behavior of crystals. Philosophical Magazine A72, 415-451.
26. Zienkiewicz, O.C., Zhu, J.Z., 1987. A simple error estimator and adaptive procedure for practical engineering analysis. International Journal of Numerical Methods in Engineering 24, 337-357.