On numerical aspects of phase field fracture modelling

European Physical Journal Plus

Volumn 126, Issue 10, 2011, Pages 1-16

  Pilipenko, D ^a   Fleck, M ^a   Emmerich, H ^a  

^a UNIVERSITY OF BAYREUTH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84860800380     PISSN: None     EISSN: 21905444     Source Type: Journal    
DOI: 10.1140/epjp/i2011-11100-3     Document Type: Article

References (32)

1. A.A. Griffith, Phil. Trans. R. Soc. A 221, 163 (1921).
2. L.B. Freund, Dynamic Fracture Mechanics, first edition, Cambridge Monographs on Mechanics and Applied Mathematics (Cambridge University Press, NY, 1998).
3. J. Fineberg, M. Marder, Phys. Rep. 313, 1 (1999).
4. F.F. Abraham, Phys. Rev. Lett. 77, 869 (1996).
5. F. Cleri, S. Yip, D. Wolf, S.R. Phillpot, Phys. Rev. Lett. 79, 1309 (1997).
6. S.J. Zhou, D.M. Beazley, P.S. Lomdahl, B.L. Holian, Phys. Rev. Lett. 78, 479 (1997).
7. M.J. Buehler, H. Gao, Nature 439, 307 (2006).
8. J. Hauch et al., Phys. Rev. Lett. 82, 3823 (1999).
9. E.A. Brener, R. Spatschek, Phys. Rev. E 67, 016112 (2003).
10. R. Spatschek, E. Brener, D. Pilipenko, Phys. Rev. Lett. 101, 205501 (2008).
11. M. Fleck, D. Pilipenko, R. Spatschek, E.A. Brener, Phys. Rev. E 83, 046213 (2011).
12. I.S. Aranson, V.A. Kalatsky, V.M. Vinokur, Phys. Rev. Lett. 85, 118 (2000).
13. A. Karma, D. Kessler, H. Levine, Phys. Rev. Lett. 87, 045501 (2001).
14. L. Eastgate et al., Phys. Rev. E 65, 036117 (2002).
15. A. Karma, A. Lobkovsky, Phys. Rev. Lett. 92, 245510 (2004).
16. H. Henry, H. Levine, Phys. Rev. Lett. 93, 105504 (2004).
17. V.I. Marconi, E.A. Jagla, Phys. Rev. E 71, 036110 (2005).
18. R. Spatschek, M. Hartmann, E. Brener, H. Müller-Krumbhaar, K. Kassner, Phys. Rev. Lett. 96, 015502 (2006).
19. R. Spatschek, C. Müller-Gugenberger, E. Brener, B. Nestler, Phys. Rev. E 75, 066111 (2007).
20. R. Spatschek, E.A. Brener, A. Karma, Phil. Mag. 91, 75 (2011).
21. W. Bangerth, R. Hartmann, G. Kanschat, ACM Trans. Math. Softw 33, 24 (2007).
22. R.J. Asaro, W.A. Tiller, Metall. Tran. 3, 1789 (1972).
23. M.A. Grinfeld, Sov. Phys. Dokl. 31, 831 (1986).
24. D.J. Srolovitz, Acta Metall. 37, 621 (1989).
25. L.D. Landau, E.M. Lifshitz, Theory of Elasticity (Pergamon Press, Oxford, 1987).
26. K. Kassner et al., Phys. Rev. E 63, 036117 (2001).
27. C. Gugenberger, R. Spatschek, K. Kassner, Phys. Rev. E 78, 016703 (2008).
28. D. Pilipenko, R. Spatschek, E.A. Brener, H. Müller-Krumbhaar, Phys. Rev. Lett. 98, 015503 (2007).
29. J.R. Rice, Mathematical analysis in the mechanics of fracture, in Fracture: An Advanced Treatise, edited by H. Liebowitz, Vol. 2 (Academic, NY, 1968) Chapt. 3, p. 192.
30. M.J.D. Powell, Numerical Method for Nonlinear Algebraic Equations, edited by P. Rabinowitz (Cordon and Breach, London, 1970).
31. J.E Dennis, Jr., R.B. Shnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, NY, 1983).
32. T.-S. Lo, A. Pomyalov, I. Procaccia, J. Zylberg, Phys. Rev. E 78, 027101 (2008).