Extensions of fibre bundle models

Lecture Notes in Physics

Volumn 705, Issue , 2006, Pages 57-92

  Kun, Feri ^a   Raischel, F ^b   Hidalgo, R C ^c   Herrmann, H J ^b  

^a UNIVERSITY OF DEBRECEN   (Hungary)

^b UNIVERSITY OF STUTTGART   (Germany)

^c UNIVERSITY OF BARCELONA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749186496     PISSN: 00758450     EISSN: None     Source Type: Book Series    
DOI: 10.1007/3-540-35375-5_3     Document Type: Article

References (72)

1. M.P. Allen and D.J. Tildesley, Editors, Computer Simulation of Liquids, Oxford University Press, Oxford (1984).
2. J.V. Andersen, D. Sornette, and K. Leung, Tricritical Behaviour in Rupture Induced by Disorder, Phys. Rev. Lett., 78 2140-2143 (1997).
3. G.G. Batrouni and A. Hansen, Fracture in three-dimensional fuse networks, Phys. Rev. Lett., 80 325 (1998).
4. G.G. Batrouni, A. Hansen, and J. Schmittbuhl, Heterogeneous interfacial failure between two elastic blocks, Phys. Rev. E, 65 036126 (2002).
5. P. Bhattacharyya, S. Pradhan, and B.K. Chakrabarti, Phase transition in fibre bundle models with recursive dynamics, Phys. Rev. E, 67(14) 046122 (2003).
6. B.K. Chakrabarti and L.G. Benguigui, Statistical Physics of Fracture and Breakdown in Disordered Systems, Oxford University Press, Oxford (1997).
7. B.D. Coleman, Time dependence of mechanical breakdown phenomena, J. Appl. Phys., 27 862 (1956).
8. W.A. Curtin, The "tough" to brittle transition in brittle matrix composites, J. Mech. Phys. Solids, 41 217 (1993).
9. W.A. Curtin, Size Scaling of Strength in Heterogeneous Materials, Phys. Rev. Lett., 80 1445-1448 (1998).
10. D.-H. Kim, B.J. Kim, and H. Jeong, Universality class of the fibre bundle model on complex networks, Phys. Rev. Lett., 94 025501 (2005).
11. Ravá da Silveira, An introduction to breakdown phenomena in disordered systems, Am. J. Phys., 67 1177 (1999).
12. H.E. Daniels, The statistical theory of the strength of bundles of threads-I, Proc. R. Soc. London A, 183 405-435 (1945).
13. A. Delaplace, S. Roux, and G. Pijaudier-Cabot, Damage cascade in a softening interface, Int. J. Solids Struct., 36 1403-1426 (1999).
14. A. Delaplace, S. Roux, and G. Pijaudier-Cabot, Avalanche Statistics of Interface Crack Propagation in Fibre Bundle Model: Characterization of Cohesive Crack, J. Eng. Mech., 127 646-652 (2001).
15. G. Dill-Langer, R.C. Hidalgo, F. Kun, Y. Moreno, S. Aicher, and H.J. Herrmann, Size dependency of tension strength in natural fibre composites, Physica A, 325 547-560 (2003).
16. A.G. Evans and F.W. Zok, The physics and mechanics of fibre-reinforced brittle matrix composites, Journal of Materials Science, 29 3857-3896 (1994).
17. J.B. Gómez, D. Iñiguez, and A.F. Pacheco, Solvable Fracture Model with Local Load Transfer, Phys. Rev. Lett., 71 380 (1993).
18. A. Hansen and P.C. Hemmer, Burst Avalanches in Bundles of Fibres: Local Versus Global Load-Sharing, Phys. Lett. A, 184 394-396 (1994).
19. A. Hansen and S. Roux, Statistical toolbox for damage and fracture. In D. Krajcinovic and J. van Mier, Editors, Damage and Fracture of Disordered Materials, number 410 in CISM Courses and Lectures, Chap. 2, pp. 17-101. Springer Verlag (2000).
20. D.G. Harlow and S.L. Phoenix, The Chain-of-Bundles Probability Model For the Strength of Fibrous Materials i: Analysis and Conjectures, J. Composite Materials, 12 195 (1978).
21. D.G. Harlow and S.L. Phoenix, The Chain-of-Bundles Probability Model for the Strength of Fibrous Materials ii: A Numerical Study of Convergence, J. Composite Materials, 12 314 (1978).
22. P.C. Hemmer and A. Hansen, The Distribution of Simultaneous Fibre Failures in Fibre Bundles, J. Appl. Mech., 59 909-914 (1992).
23. H.J. Herrmann and S. Roux, Editors, Statistical models for the fracture of disordered media, Random materials and processes, Elsevier, Amsterdam (1990).
24. R.C. Hidalgo, F. Kun, and H.J. Herrmann, Bursts in a fibre bundle model with continuous damage, Phys. Rev. E, 64(6) 066122 (2001).
25. R.C. Hidalgo, F. Kun, and H.J. Herrmann, Creep rupture of viscoelastic fibre bundles, Phys. Rev. E, 65 032502 (2002).
26. R.C. Hidalgo, Y. Moreno, F. Kun, and H. J. Herrmann, Fracture model with variable range of interaction, Phys. Rev. E, 65 046148 (2002).
27. B.J. Kim, Phase transitions in the modified fibre bundle model, Europhys. Letts., 66 819 (2004).
28. M. Kloster, A. Hansen, and P.C. Hemmer, Burst avalanches in solvable models of fibrous materials, Phys. Rev. E, 56 2615-2625 (1997).
29. J. Knudsen and A.R. Massih, Breakdown of disordered media by surface loads, Phys. Rev. E, 72 036129 (2005).
30. F. Kun and H.J. Herrmann, Damage development under gradual loading of composites, Journal of Materials Science, 35 4685 (2000).
31. F. Kun, R.C. Hidalgo, H.J. Herrmann, and K.F. Pal, Scaling laws of creep rupture of fibre bundles, Phys. Rev. E, 67(6) 061802 (2003).
32. F. Kun, Y. Moreno, R.C. Hidalgo, and H.J. Herrmann, Creep rupture has two universality classes, Europhys. Lett., 63(3) 347-353 (2003).
33. F. Kun, S. Zapperi, and H. J. Herrmann, Damage in fibre bundle models, Eur. Phys. J. B, 17 269 (2000).
34. L. Moral, J.B. Gomez, and Y. Moreno, Exact numerical solution for a time-dependent fibre-bundle model with continuous damage, J. Phys. A-Math. Gen., 34 9983 (2001).
35. L. Moral, Y. Moreno, J.B. Gomez, and A.F. Pacheco, Time dependence of breakdown in a global fibre-bundle model with continuous damage, Phys. Rev. F, 63 066106 (2001).
36. Y. Moreno, J.B. Gómez, and A.F. Pacheco, Self-organized criticality in a fibre-bundle-type model, Physica A, 274 400 (1999).
37. Y. Moreno, J.B. Gomez, and A.F. Pacheco, Fracture and second-order phase transitions, Phys. Rev. Lett., 85(14) 2865-2868 (2000).
38. Y. Moreno, J.B. Gomez, and A.F. Pacheco, Instability of scale-free networks under node-breaking avalanches, Eur. Phys. Lett., 58 630 (2002).
39. H. Nechad, A. Helmstetter, R. El Guerjouma, and D. Sornette, Andrade and critical time to failure laws in fibre-matrix composites: Experiments and model J. Mech. Phys. Solids, 53 1099 (2005).
40. H. Nechad, A. Helmstetter, R. El Guerjouma, and D. Sornette, Creep ruptures in heterogeneous materials, Phys. Rev. Lett., 94 045501 (2005).
41. W.I. Newman and A.M. Gabrielov, Failure of hierarchical distributions of fibre bundles, International Journal of Fracture, 50 1-14 (1991).
42. W.I. Newman, D.L. Turcotte, and A.M. Gabrielov, log-periodic behavior of a hierarchical failure model with applications to precursory seismic activation, Phys. Rev. E, 52 4827 (1995).
43. P.K. Nukala and S. Simunovic, A continuous damage random thresholds model for simulating the fracture behavior of nacre, Biomaterials, 26 6087 (2005).
44. P.K. Nukala and S.Simunovic, Statistical physics models for nacre fracture simulation, Phys. Rev. E, 72 041919 (2005).
45. P.V.V. Nukala, S. Simunovic, and S. Zapperi, Percolation and localization in the random fuse model, J. Stat. Mech: Theor. Exp., p. P08001 (2004).
46. F.T. Peires, Tensile tests for cotton yarns. v.-'the weakest link', theorems on the strength of long composite specimens, J. Textile Inst., 17 T355-368 (1926).
47. S.L. Phoenix and I.J. Beyerlein, Statistical Strength Theory for Fibrous Composite Materials, volume 1 of Comprehensive Composite Materials, Sect. 1.19, pages 1-81. Pergamon, Elsevier Science, N. Y. (2000).
48. S.L. Phoenix, M. Ibnabdeljalil, and C.-Y. Hui, Int. J. Solids Structures, 34 545 (1997).
49. S.L. Phoenix and I.J. Beyerlein, Statistical Strength Theory for Fibrous Composite Materials, In A. Kelly and C. Zweben, Editors, Comprehensive Composite Materials, Vol. 1, Sect. 1.19. Pergamon, Elsevier Science, New York (2000).
50. S.L. Phoenix and R. Raj, Scalings in fracture probabilities for a brittle matrix fibre composite, Acta metall. mater., 40 2813 (1992).
51. S. Pradhan and B.K. Chakrabarti, Precursors of catastrophe in the Bak-Tang-Wiesenfeld, Manna, and random-fibre-bundle models of failure, Phys. Rev. E, 65 016113 (2002).
52. S. Pradhan and B.K. Chakrabarti, Failure due to fatigue in fibre bundles and solids, Phys. Rev. E, 67(14) 046124 (2003).
53. S. Pradhan and B. K. Chakrabarti, Failure properties of fibre bundle models, Int. J. Mod. Phys. B, 17 5565-5581 (2003).
54. S. Pradhan, A. Hansen, and P.C. Hemmer, Crossover behavior in burst avalanches: Signature of imminent failure, Phys. Rev. Lett., 95 125501 (2005).
55. S. Pradhan, A. Hansen, and P.C. Hemmer, Crossover behavior in burst avalanches: Signature of imminent failure, Phys. Rev. Lett., 95 125501 (2005).
56. S. Pradhan and A. Hansen, Failure properties of loaded fibre bundles having a lower cutoff in fibre threshold distribution, Phys. Rev. E, 72 026111 (2005).
57. S.R. Pride and R. Toussaint, Thermodynamics of fibre bundles, Physica A, 312 159-171 (2002).
58. F. Raischel, F. Kun, and H.J. Herrmann, Simple beam model for the shear failure of interfaces, Phys. Rev. E, 72 046126 (2005).
59. S. Roux, Thermally activated breakdown in the fibre-bundle model, Phys. Rev. E, 62 6164 (2000).
60. S. Roux, A. Delaplace, and G. Pijaudier-Cabot, Damage at heterogeneous interfaces, Physica A, 270 35-41 (1999).
61. R. Scorretti, S. Cilibreto, and A Guarino, Disorder enhances the effect of thermal of thermal noise in the fibre bundle model, Europhys. Lett., 55 626-632 (2001).
62. D. Sornette, Elasticity and failure of a set of elements loaded in parallel, J. Phys. A, 22 L243-L250 (1989).
63. D. Sornette, Mean-field solution of a block-spring model of earthquakes, J. Phys. I. France, 2 2089 (1992).
64. D. Sornette. Statistical physics of rupture in heterogeneous media. In S. Yip, editor, Handbook of Materials Modeling, Sect. 4.4. Springer Science and Business Media (2005).
65. D. Sornette and J.V. Andersen, Scaling with respect to disorder in time-to-failure, Eur. Phys. J. B, 1 353 (1998).
66. R. Toussaint and S.R. Pride, Interacting damage models mapped onto Ising and percolation models, Phys. Rev. E, 71 046127 (2005).
67. D.L. Turcotte and M.T. Glasscoe, A damage model for the continuum rheology of the upper continental crust, Tectonophysics, 383 71-80 (2004).
68. E. Vives and A. Planes, Avalanches in a fluctuationless first-order phase transition in a random-bond ising model, Phys. Rev. B, 50 3839 (1994).
69. S. Zapperi, P. Ray, H.E. Stanley, and A. Vespignani, First-Order Transition in the Breakdown of Disordered Media, Phys. Rev. Lett., 78 1408 (1997).
70. S. Zapperi, P. Ray, H.E. Stanley, and A. Vespignani, Analysis of damage clusters in fracture processes, Physica A, 270 57 (1999).
71. S. Zapperi, P. Ray, H.E. Stanley, and A. Vespignani, Avalanches in breakdown and fracture processes, Phys. Rev. E, 59 5049 (1999).
72. S. Zapperi, A. Vespignani, and H.E. Stanley, Plasticity and avalanche behaviour in microfracturing phenomena, Nature, 388 658 (1997).