Phase field modeling of fracture and stress-induced phase transitions

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 75, Issue 6, 2007, Pages

  Spatschek, R ^a   Muller Gugenberger C ^a   Brener, E ^a   Nestler, B ^b  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b KARLSRUHE UNIVERSITY OF APPLIED SCIENCES   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; CONTINUUM MECHANICS; FRACTURE; KINETICS; MATHEMATICAL MODELS; STRESS ANALYSIS;

ASARO-TILLER-GRINFELD INSTABILITY; CONTINUUM THEORY; ELASTIC EQUATIONS; PHASE FIELD MODELING;

PHASE TRANSITIONS;

EID: 34547281948     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.75.066111     Document Type: Article

References (29)

1. A. A. Griffith, Philos. Trans. R. Soc. London, Ser. A PTRMAD 0962-8428 21, 163 (1921).
2. L. B. Freund, Dynamic Fracture Mechanics (Cambridge University Press, Cambridge, England, 1998).
3. J. A. Hauch, D. Holland, M. P. Marder, and H. L. Swinney, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.82.3823 82, 3823 (1999).
4. J. S. Langer, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.1351 62, 1351 (2000).
5. A. Livne, O. Ben-David, and J. Fineberg, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.124301 98, 124301 (2007).
6. A. Karma, D. A. Kessler, and H. Levine, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.045501 87, 045501 (2001);
7. A. Karma and A. E. Lobkovsky, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.245510 92, 245510 (2004).
8. H. Henry and H. Levine, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.105504 93, 105504 (2004).
9. I. S. Aranson, V. A. Kalatsky, and V. M. Vinokur, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.85.118 85, 118 (2000).
10. L. O. Eastgate, J. P. Sethna, M. Rauscher, T. Cretegny, C. S. Chen, and C. R. Myers, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65.036117 65, 036117 (2002).
11. K. Kassner, C. Misbah, J. Müller, J. Kappey, and P. Kohlert, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.63.036117 63, 036117 (2001).
12. V. I. Marconi and E. A. Jagla, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.036110 71, 036110 (2005).
13. E. A. Brener and R. Spatschek, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.67.016112 67, 016112 (2003).
14. J. Fineberg and M. Marder, Phys. Rep. PRPLCM 0370-1573 10.1016/S0370-1573(98)00085-4 313, 1 (1999).
15. R. J. Asaro and W. A. Tiller, Metall. Trans. MTGTBF 0026-086X 3, 1789 (1972);
16. M. A. Grinfeld, Sov. Phys. Dokl. SPHDA9 0038-5689 31, 831 (1986).
17. R. Spatschek, M. Hartmann, E. Brener, H. Müller-Krumbhaar, and K. Kassner, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.015502 96, 015502 (2006).
18. D. Pilipenko, R. Spatschek, E. A. Brener, and H. Müller-Krumbhaar, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.015503 98, 015503 (2007).
19. E. A. Brener, V. Marchenko, and R. Spatschek, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.75.041604 75, 041604 (2007).
20. W. H. Yang and D. J. Srolovitz, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.71.1593 71, 1593 (1993);
21. B. J. Spencer and D. I. Meiron, Acta Metall. Mater. AMATEB 0956-7151 10.1016/0956-7151(94)90429-4 42, 3629 (1994);
22. K. Kassner and C. Misbah, Europhys. Lett. EULEEJ 0295-5075 28, 245 (1994).
23. A. Rätz, A. Ribalta, and A. Voigt, J. Comput. Phys. JCTPAH 0021-9991 10.1016/j.jcp.2005.09.013 214, 187 (2006).
24. B. Nestler, H. Garcke, and B. Stinner, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.041609 71, 041609 (2005).
25. H. Garcke, B. Nestler, and B. Stoth, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(97)00227-3 115, 87 (1998);
26. H. Garcke, B. Nestler, and B. Stoth, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139998334895 60, 295 (1999).
27. I. A. Privorotskii, Sov. Phys. JETP SPHJAR 0038-5646 33, 825 (1971).
28. P. Nozières, J. Phys. I JPGCE8 1155-4304 10.1051/jp1:1993108 3, 681 (1993).
29. J. Virieux, Geophysics GPYSA7 0016-8033 10.1190/1.1442147 51, 889 (1986).