Dynamics of steps along a martensitic phase boundary II: Numerical simulations

Journal of the Mechanics and Physics of Solids

Volumn 56, Issue 2, 2008, Pages 521-541

  Zhen, Yubao ^a   Vainchtein, Anna ^b  

^a HARBIN INSTITUTE OF TECHNOLOGY   (China)

^b UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

Cascade nucleation; Interphase step; Non reflecting boundary condition; Sequential motion; Supersonic motion

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; MATHEMATICAL MODELS; NUCLEATION; STRESS-STRAIN CURVES;

CASCADE NUCLEATION; NON-REFLECTING BOUNDARY CONDITION; SEQUENTIAL MOTION; SUPERSONIC MOTION;

MARTENSITIC TRANSFORMATIONS;

EID: 38849084588     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.05.018     Document Type: Article

References (31)

1. Adelman S., and Doll J. Generalized Langevin equation approach for atom/solid-surface scattering: collinear atom/harmonic chain model. J. Chem. Phys. 61 (1974) 4242-4245
2. Bayliss A., and Turkel E. Radiation boundary conditions for wave-like equations. Commun. Pure Appl. Math. 33 (1980) 707-725
3. Cai W., Koning M., Bulatov V., and Yip S. Minimizing boundary reflections in coupled-domain simulations. Phys. Rev. Lett. 85 15 (2000) 3213-3216
4. Cserti J. Application of the lattice Green's function for calculating the resistance of infinite networks of resistors. Am. J. Phys. 68 (2000) 896-906
5. Engquist B., and Majda A. Absorbing boundary conditions for the numerical simulation of waves. Math. Comput. 31 (1977) 629-651
6. Engquist B., and Majda A. Absorbing boundary conditions for acoustic and elastic wave calculations. Commun. Pure Appl. Math. 32 (1979) 313-357
7. Flytzanis N., Celli V., and Nobile A. Motion of two screw dislocations in a lattice. J. Appl. Phys. 45 12 (1974) 5176-5181
8. Givoli D. Non-reflecting boundary conditions. J. Comput. Phys. 94 (1991) 1-29
9. Givoli D. Exact representations on artificial interfaces and applications in mechanics. Appl. Mech. Rev. 52 (1999) 333-349
10. Glasser M., and Boersma J. Exact values for the cubic lattice Green functions. J. Phys. A Math. Gen. 33 (2000) 5017-5023
11. Grote M., and Keller J. Exact nonreflecting boundary conditions for the time dependent wave equation. SIAM J. Appl. Math. 55 2 (1995) 280-297
12. Grote M., and Keller J. On nonreflecting boundary conditions. J. Comput. Phys. 122 (1995) 231-243
13. Hagstrom T. Radiation boundary conditions for the numerical simulation of waves. In: Iserles A. (Ed). Acta Numerica vol. 8 (1999), Cambridge University Press, Cambridge 47-106
14. Higdon R.L. Absorbing boundary conditions for difference approximations to the multi-dimensional wave equation. Math. Comput. 47 176 (1986) 437-459
15. Higdon R.L. Radiation boundary conditions for elastic wave propagations. SIAM J. Numer. Anal. 27 4 (1990) 831-870
16. Ishioka S. Stress field around a high speed screw dislocation. J. Phys. Chem. Solids 36 (1975) 427-430
17. Karpov E., Wagner G., and Liu W. A Green's function approach to deriving non-reflecting boundary conditions in molecular dynamics simulations. Int. J. Numer. Methods Eng. 62 9 (2005) 1250-1262
18. Katsura S., and Inawashiro S. Lattice Green's functions for the rectangular and the square lattices at arbitrary points. J. Math. Phys. 12 8 (1971) 1622-1630
19. Katsura S., Morita T., Inawashiro S., Horiguchi T., and Abe Y. Lattice Green's function. Introduction. J. Math. Phys. 12 5 (1971) 892-895
20. Koizumi H., Kirchner H., and Suzuki T. Lattice waves emission from a moving dislocation. Phys. Rev. B 65 (2002) 214104
21. Li X., and E W. Variational boundary conditions for molecular dynamics simulations of solids at low temperature. Commun. Comput. Phys. 1 1 (2006) 135-175
22. Lubich C., and Schädle A. Fast convolution for nonreflecting boundary conditions. SIAM J. Sci. Comput. 24 1 (2002) 161-182
23. Morita T. Useful procedure for computing the lattice Green's function-square, tetragonal, and bcc lattices. J. Math. Phys. 12 8 (1971) 1744-1747
24. Murli A., and Rizzardi M. ALGORITHM 682: Talbot's method for the Laplace inversion problem. ACM Trans. Math. Software 16 2 (1990) 158-168
25. Park H., Karpov E., Liu W., and Klein P. The bridging scale for two-dimensional atomistic/continuum coupling. Philos. Mag. 85 (2005) 79-113
26. Ryaben'kii V., Tsynkov S., and Turchaninov V. Global discrete artificial boundary conditions for time-dependent wave propagation. J. Comput. Phys. 174 (2001) 712-758
27. Teng Z.-H. Exact boundary condition for time-dependent wave equation based on boundary integral. J. Comput. Phys. 190 (2003) 398-418
28. Tewary V. Computationally efficient representation for elastostatic and elastodynamic Green's functions for anisotropic solids. Phys. Rev. B 51 22 (1995) 15695-15702
29. Tsynkov S. Numerical solution of problems on unbounded domains. A review. Appl. Numer. Math. 27 (1998) 465-532
30. Wagner G., Karpov E., and Liu W. Molecular dynamics boundary conditions for regular crystal lattice. Comput. Method Appl. Mech. Eng. 193 (2004) 1579-1601
31. Zhen, Y., Vainchtein, A., 2007. Dynamics of steps along a martensitic phase boundary I: Semi-analytical solution. J. Mech. Phys. Solids, doi:10.1016/j.jmps.2007.05.017.