Lattice Green's functions in nonlinear analysis of defects

Journal of Applied Mechanics, Transactions ASME

Volumn 74, Issue 4, 2007, Pages 686-690

  Haq, S ^a   Movchan, A B ^b   Rodin, G J ^c  

^a THE UNIVERSITY OF AGRICULTURE   (Pakistan)

^b UNIVERSITY OF LIVERPOOL   (United Kingdom)

^c UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; GREEN'S FUNCTION; IMPULSE RESPONSE; LINEAR ALGEBRA; NONLINEAR ANALYSIS; PROBLEM SOLVING;

HYBRID FINITE-BOUNDARY ELEMENT METHODS; LINEAR REGIONS;

SURFACE DEFECTS;

EID: 34548273537     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2710795     Document Type: Article

References (22)

1. Martinsson, P. G., and Rodin, G. J., 2003, "Boundary Algebraic Equations for Lattice Problems," IUTAM Symposium on Asymptotics, Singularities and Ho_mogenisation in Problems of Mechanics, Proceedings of the IUTAM Symposium, Liverpool, UK, July 8-11, A. B. Movchan, ed., pp. 191-198.
2. Masudajindo, K., Tewary, V. K., and Thomson, R., 1991, "Theoretical Study of the Fracture of Brittle Materials: Atomistic Calculations Materials," Mater. Sci. Eng., A, 146(1-2), pp. 273-289.
3. Masudajindo, K., Tewary, V. K., and Thomson, R., 1991, "Atomic Theory of Fracture of Brittle Materials: Application to Covalent Semiconductors," J. Mater. Res. 6(7), pp. 1553-1566.
4. Thomson, R., Zhou, S, J., Carlsson, A. E., and Tewary, V. K., 1992, "Lattice Imperfections Studied by Use of Lattice Green-Functions," Phys. Rev. B, 46(17), pp. 10613-10622.
5. Zhou, S. J., Carlsson, A. E., and Thomson, R., 1993, "Dislocation Nucleation and Crack Stability-Lattice Greens-Function Treatment of Cracks in a Model Hexagonal Lattice," Phys. Rev. B, 47(13), pp. 7710-7719.
6. Zhou, S. J., and Curtin, W. A., 1995, "Failure of Fiber Composites: A Lattice Green-Function Model," Acta Metall. Mater., 43(8), pp. 3093-3104.
7. Schiotz, J., and Carlsson, A. E., 1997, "Calculation of Elastic Green's Functions for Lattices with Cavities," Phys. Rev. B, 56(5), pp. 2292-2294.
8. Rao, S., Hernandez, G., Simmons, J. P., Parthasarathy, T. A., and Woodward, C., 1998, "Green's Function Boundary Conditions in Two-Dimensional and Three-Dimensional Atomistic Simulations of Dislocations," Philos. Mag. A, 77(1), pp. 231-256.
9. Masuda-Jindo, K., Menon, M., and Van Hung, V., 2001, "Atomistic Study of Fracture of Nanoscale Materials by Molecular Dynamics and Lattice Green's Function Methods," J. Phys. IV, 11(PR5), pp. 11-18.
10. Wang, S., 2002, "Lattice Theory for Structure of Dislocations in a Two-Dimensional Triangular Crystal," Phys. Rev. B, 65(9), p. 094111.
11. Saito, Y., 2004, "Elastic Lattice Green's Function in Three Dimensions," J. Phys. Soc. Jpn., 73, pp. 1816-1826.
12. Saltzer, C., 1958, "Discrete Potential Theory for Two-Dimensional Laplace and Poisson Difference Equations," Paper No. NACA TN 4086.
13. Greengard, L., and Rokhlin, V., 2003, "A New Version of the Fast Multipole Method for the Laplace Equation in Three Dimensions," Acta Numerica, 6, pp. 229-269.
14. Nishimura, N., 2002, "Fast Multipole Accelerated Boundary Integral Equation Methods," Appl. Mech. Rev., 55, pp. 299-324.
15. Martinsson, P. G., and Rodin, G. J., 2003, "Asymptotic Expansions of Lattice Green's Functions," Proc. R. Soc. London, Ser. A, 458(2027), pp. 2609-2622.
16. Necas, J., and Hlavacek, J., 1981, Mathematical Theory of Elastic and Elasto-Plastic Bodies: An Introduction, Elsevier/North Holland, Amsterdam, Netherlands.
17. Bonnet, M., 1999, Boundary Integral Equation Methods for Solids and Fluids, Wiley, New York.
18. Duffin, R. J., and Shelly, E. P., 1958, "Difference Equations of Polyharmonic Type," Duke Math. J., 25, pp. 209-238.
19. Frenkel, J., and Kontorova, T., 1938, "On the Theory of Plastic Deformation and Twinning," J. Exp. Theor. Phys., 8, pp. 89-91.
20. Peierls, R., 1940, "The Size of a Dislocation," Proc. Phys. Soc. London, 52, pp. 34-37.
21. Nabarro, F. R. N., 1947, "Dislocations in a Simple Cubic Lattice," Proc. Phys. Soc. London, 59, pp. 256-272.
22. Haq, S., Movchan, A. B., and Rodin, G. J., 2006, "Analysis of Lattices With Non-Linear Interphases," Acta Mech. Sin., 22, pp. 323-330.