An adaptive finite element approach to atomic-scale mechanics—the quasicontinuum method
Tài liệu tham khảo
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.
Barenblatt, G.I., 1962. The mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics, 7, 55–129.
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.
Chadwick, P., 1976. Continuum Mechanics. John Wiley and Sons, New York.
Christian, J. W. (1983) Some surprising features of the plastic deformation of body-centered cubic metals and alloys. Metallurgical Transactions A14, 1237–1256.
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.
Daw, M.S., Baskes, M.I., 1983. Semiempirical, quantum-mechanical calculations of hydrogen embrittlement in metals. Physical Review Letters 50, 1285–1288.
Dennis, J.E. Jr., Schnabel, R.B., 1983. Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs.
Ercolessi, F., Adams, J., 1993. Interatomic potentials from 1st-principles calculations—the force-matching method. Europhysics Letters 26, 583–588.
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.
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.
Hirth, J.P., Lothe, J., 1968. Theory of Dislocations. McGraw–Hill, New York.
Hull, D., Bacon, D.J., 1992. Introduction to Dislocations. Pergamon Press, Oxford.
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.
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.
Okabe, A., Boots, B., Sugihara, K., 1992. Spatial Tessellations. Wiley and Sons, New York.
Papadrakakis, M., Ghionis, P., 1986. Conjugate-gradient algorithms in nonlinear structural-analysis problems. Computer Methods in Applied Mechanics Engineering 59, 11–27.
Peierls, R.E., 1940. The size of a dislocation. Proceedings of the Physical Society of London 52, 34–37.
Shenoy, V.B., Phillips, R., 1997. Finite-sized atomistic simulations of screw dislocations. Philosophical Magazine A76, 367–385.
Sloan, S.W., 1993. A fast algorithm for generating constrained Delaunay triangulations. Computers and Structures 47, 441–450.
Tadmor, E.B., 1996. The quasicontinuum method. Ph.D. Thesis, Brown University.
Tadmor, E.B., Ortiz, M., Phillips, R., 1996. Quasicontinuum analysis of defects in solids. Philosophical Magazine A73, 1529–1563.
Tadmor, E.B., Miller, R., Phillips, R., Ortiz, M., 1997. Quasicontinuum analysis of nanoindentation. To be submitted to Acta Materiala.
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.
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.
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.