References
- da Vinci , L . 1940 . I libri di Meccanica , Milano : Hoepli .
- Galilei , G . 1958 . Discorsi e Dimostrazioni Matematiche Intorno a due Nuove Scienze , Torino : Boringhieri .
- Parsons , WB . 1939 . Engineers and Engineering in the Renaissance , Cambridge : MIT Press .
- Lund , JR and Byrne , JP . 2001 . Civil. Eng. Env. Syst. , 18 : 243
- Griffith , AA . 1920 . Trans. Roy. Soc. (London) A , 221 : 163
- Weibull , W . 1939 . A Statistical Theory of the Strength of Materials , Stockholm : Generalstabens litografiska anstalts förlag .
- Timoshenko , SP . 1953 . History of Strength of Materials , New York : McGraw-Hill .
- Herrmann , HJ and Roux , S . 1990 . Statistical Models for the Fracture of Disordered Media , Amsterdam : North-Holland .
- Chakrabarti , BK and Benguigui , LG . 1997 . Statistical Physics of Fracture and Breakdown in Disordered Systems , Oxford : Oxford Science Publications .
- Hansen , A and Roux , S . 2000 . Statistical Toolbox for Damage and Fracture , 17 – 101 . New York : Springer-Verlag .
- Mishnaevsky , JLL . 1997 . Eng. Fract. Mech. , 56 : 47
- de Arcangelis , L , Redner , S and Herrmann , HJ . 1985 . J. Phys. (Paris) Lett. , 46 : 585
- Pierce , FT . 1926 . J. Textile Inst. , 17 : 355
- Daniels , HE . 1945 . Proc. R. Soc. London A , 183 : 405
- Krajcinovic , D and van Mier , JGM . 2000 . Damage and Fracture of Disordered Materials , New York : Springer-Verlag .
- van Mier , JGM . 1996 . Fracture Processes of Concrete , Boca Raton, , USA : CRC Press .
- Bazant , ZP and Planas , J . 1997 . Fracture and Size Effect in Concrete and Other Quasibrittle Materials , Boca Raton, , USA : CRC Press .
- van Mier , JGM and van Vliet , MRA . 2003 . Eng. Fract. Mech. , 70 : 2281
- Lilliu , G and van Mier , JGM . 2003 . Eng. Fract. Mech. , 70 : 927
- Schlangen , E and Garboczi , EJ . 1996 . Int. J. Eng. Sci. , 34 : 1131
- Niemeyer , L , Pietronero , L and Wiesmann , HJ . 1984 . Phys. Rev. Lett. , 52 : 1033
- Beale , PD and Duxbury , PM . 1988 . Phys. Rev. B , 37 : 2785
- Arndt , PF and Nattermann , T . 2001 . Phys. Rev. B , 63 : 134204
- Lemaitre , J and Chaboche , JL . 1990 . Mechanics of Solid Materials , Cambridge : Cambridge University Press .
- Krajcinovic , D . 1996 . Damage Mechanics , Amsterdam : Elsevier .
- Gluzman , S and Sornette , D . 2001 . Phys. Rev. E , 63 : 066129
- Shcherbakov , R and Turcotte , DL . 2003 . Theor. Appl. Frac. Mech. , 39 : 245
- Atkinson , BK and Meredith , PG . 1987 . 110 New York : Academic Press .
- Straumsnes , S , Dommersnes , P , Flekkoy , EG and Roux , S . 1997 . European J. Mech. A-Sol. , 16 : 993
- Barenblatt , GI . 1996 . Scaling, Self-Similarity and Intermediate Asymptotics , Cambridge : Cambridge University Press .
- Family , F and Viscek , T . 1991 . Dynamics of Fractal Surfaces , Singapore : World Scientific .
- Barabási , A.-L and Stanley , HE . 1995 . Fractal Concepts in Surface Growth , Cambrdige : Cambridge University Press .
- Lopez , JM , Rodriguez , MA and Cuerno , R . 1997 . Phys. Rev. E , 56 : 3993
- Lopez , JM . 1999 . Phys. Rev. Lett. , 83 : 4594
- Nattermann , T , Stepanow , S , Tang , LH and Leschhorn , H . 1992 . J. Phys. (France) II , 2 : 1483
- Leschhorn , H , Nattermann , T , Stepanow , S and Tang , LH . 1997 . Ann. Physik , 7 : 1
- Narayan , O and Fisher , D . 1993 . Phys. Rev. B , 48 : 7030
- Chauve , P , Doussal , PL and Wiese , K . 2001 . Phys. Rev. Lett. , 86 : 1785
- Doussal , PL , Wiese , K and Chauve , P . 2002 . Phys. Rev. B , 66 : 174201
- Borodich , FM . 1997 . J. Mech. Phys. Sol. , 45 : 239
- Vandembroucq , D and Roux , S . 1997 . J. Mech. Phys. Sol. , 45 : 853
- Vandembroucq , D and Roux , S . 1997 . Phys. Rev. E , 55 : 6186
- Barra , F , Hentschel , HGE , Levermann , A and Procaccia , I . 2002 . Phys. Rev. E , 65 : 045101
- Barra , F , Levermann , A and Procaccia , I . 2002 . Phys. Rev. E , 66 : 066122
- Levermann , A and Procaccia , I . 2002 . Phys. Rev. Lett. , 89 : 234501
- Morel , S , Schmittbuhl , J , Bouchaud , E and Valentin , G . 2000 . Phys. Rev. Lett. , 85 : 1678
- Morel , S , Bouchaud , E and Valentin , G . 2002 . Phys. Rev. B , 65 : 104101
- Bouchaud , E and Bouchaud , J-P . 1994 . Phys. Rev. B , 50 : 17752
- Weiss , J . 2001 . Int. J. Fract. , 109 : 365
- Chiaia , B , van Mier , JGM and Vervuurt , A . 1998 . Cem. Concr. Res. , 28 : 103
- van den Born , IC , Santen , A , Hoekstra , HD and Hosson , JTMD . 1991 . Phys. Rev. B , 43 : R3794
- Bazant , ZP . 1999 . Arch. Appl. Mech. , 69 : 703
- Sutherland , L , Shenoi , R and Lewis , S . 1999 . Composite Sci. Techn. , 209 : 1999
- Korteoja , M , Salminen , LI , Niskanen , KJ and Alava , MJ . 1998 . J. Pulp Paper Sci. , 24 : 1
- Korteoja , M , Salminen , LI , Niskanen , KJ and Alava , MJ . 1999 . Mater. Sci. Eng. A , 240 : 173
- van Vliet , MRA and van Mier , JGM . 2000 . Eng. Fract. Mech. , 65 : 165
- Lu , C , Danzer , R and Fischer , FD . 2002 . Phys. Rev. E , 65 : 067102
- Doremus , RH . 1983 . J. Appl. Phys. , 54 : 193
- Lavoie , JA , Soutis , C and Morton , J . 2000 . Compos. Sci. Techn. , 60 : 283
- Foote , RML , Mai , YW and Cotterell , B . 1986 . J. Mech. Phys. Sol. , 34 : 593
- Cotterell , B and Mai , YW . 1987 . J. Mat. Sci. , 22 : 2734
- Mai , YW and Lawn , BR . 1987 . J. Am. Ceram. Soc. , 70 : 289
- Wisnom , MR . 1991 . Composites , 22 : 47
- Hu , XZ and Wittmann , F . 1992 . Mat. Struct. , 25 : 319
- Li , VC , Lin , Z and Matsumoto , T . 1998 . Int. J. Sol. Struct. , 1998 : 35
- Tabiei , A and Sun , JM . 1999 . Compos. Struct. , 46 : 209
- Wisnom , MR . 1999 . Composite Sci. Techn. , 59 : 1937
- Hu , XZ and Wittmann , F . 2000 . Eng. Fract. Mech. , 65 : 209
- Mai , YW . 2002 . Eng. Fract. Mech. , 69 : 219
- Hu , XZ . 2002 . Eng. Fract. Mech. , 69 : 555
- Stevanovic , MM , Elhisnavi , AA and Pesikan , DR . 2003 . Mat. Sci. Forum , 413 : 207
- Duan , K , Hu , XZ and Wittmann , FH . 2003 . Mat. Struct. , 36 : 74
- Bazant , ZP . 2004 . Prob. Eng. Mech. , 19 : 307
- Bazant , ZP . 2004 . PNAS , 101 : 13400
- Klock , W and Aicher , S . 2005 . Wood Fib. Sci. , 37 : 403
- Rosti , J , Salminen , LI , Seppälä , ET , Alava , MJ and Niskanen , KJ . 2001 . Eur. Phys. J. B , 19 : 259
- Bouchaud , E . 1997 . J. Phys.: Condens. Matter , 9 : 4319
- Salminen , LI , Alava , MJ and Niskanen , KJ . 2003 . Eur. Phys. J. B , 32 : 369
- Kertész , J , Horvath , VK and Weber , F . 1993 . Fractals , 1 : 67
- Engoy , T , Maloy , KJ , Hansen , A and Roux , S . 1994 . Phys. Rev. Lett. , 73 : 834
- Menezes-Sobrinho , IL , Couto , MS and Ribeiro , IRB . 2005 . Phys. Rev. E , 71 : 066121
- Bouchbinder , E , Procaccia , I and Sela , S . 2005 . Phys. Rev. Lett. , 95 : 255503
- Schmittbuhl , J and Maloy , KJ . 1997 . Phys. Rev. Lett. , 78 : 3888
- Delaplace , A , Schmittbuhl , J and Maloy , KJ . 1999 . Phys. Rev. E , 60 : 1337
- Maloy , KJ and Schmittbuhl , J . 2001 . Phys. Rev. Lett. , 87 : 105502
- Maloy , KJ , Schmittbuhl , J , Hansen , A and Batrouni , GG . 2003 . Int. J. Fract. , 121 : 9
- Maloy , KJ , Santucci , S , Schmittbuhl , J and Toussaint , R . 2006 . Phys. Rev. Lett. , 96 : 045501
- Mandelbrot , BB , Passoja , DE and Paullay , AJ . 1984 . Nature , 308 : 721
- Ponson , L , Bonamy , D and Bouchaud , E . 2006 . Phys. Rev. Lett. , 96 : 035506
- Boffa , JM , Allain , C and Hulin , J . 1998 . Eur. Phys. J. AP , 2 : 281
- Daguier , P , Nghiem , B , Bouchaud , E and Creuzet , F . 1997 . Phys. Rev. Lett. , 78 : 1062
- Bonamy , D , Ponson , L , Prades , S , Bouchaud , E and Guillot , C . 2006 . in press
- Morel , S , Lubet , T , Pouchou , J-L and Olive , J-M . 2004 . Phys. Rev. Lett. , 93 : 065504
- Plouraboue , F , Winkler , KW , Petijean , L , Hulin , J-P and Roux , S . 1996 . Phys. Rev. E , 53 : 277
- Célarié , F , Prades , S , Bonamy , D , Ferrero , L , Bouchaud , E , Guillot , C and Marliére , C . 2003 . Phys. Rev. Lett. , 90 : 075504
- Marliére , C , Prades , S , Célarié , F , Dalmas , D , Bonamy , D , Guillot , C and Bouchaud , E . 2003 . J. Phy.: Condens. Matter , 15 : S2377
- Bouchaud , JP , Bouchaud , E , Lapasset , G and Planès , J . 1993 . Phys. Rev. Lett. , 71 : 2240
- Lopez , JM and Schmittbuhl , J . 1998 . Phys. Rev. E , 57 : 6405
- Morel , S , Schmittbuhl , J , Lopez , JM and Valentin , G . 1998 . Phys. Rev. E , 58 : 6999
- Mourot , G , Morel , S , Bouchaud , E and Valentin , G . 2005 . Phys. Rev. E , 71 : 016136
- Bouchbinder , E , Procaccia , I , Santucci , S and Vanel , L . 2005 . Phys. Rev. Lett. , 96 : 055509
- Hull , D . 1999 . Fractography: Observing, Measuring and Interpreting Fracture Surface Topography , Cambridge : Cambridge University Press .
- Kouzeli , M , Weber , L , March , SC and Mortensen , A . 2001 . Acta Mater. , 49 : 497
- Kawakata , H , Cho , A , Kiyama , T , Yanagidani , T , Kusunose , K and Shimada , M . 1999 . Tectonophysics , 313 : 293
- Lockner , DA . 1993 . Int. J. Rock Mech. Min. Sci. , 30 : 883
- Berkowitz , B and Hadad , A . 1997 . J. Geophys. Res. B: Solid Earth , 102 : 12205
- Bonnet , E , Bour , O , Odling , NE , Davy , P , Main , I , Cowie , P and Berkowitz , B . 2001 . Rev. Geophys. , 39 : 347
- Rundle , J , Klein , W and Gross , S . 1999 . Pure Appl. Geophys. , 155 : 575
- Lyakhovsky , V . 2001 . Geophys. J. Int. , 144 : 114
- Goto , K and Otsuki , K . 2004 . Geophys. Res. Lett. , 31 : L05601
- Weiss , J . 1997 . Bull. Seism. Soc. Am. , 87 : 1362
- Lysak , MV . 1996 . Eng. Fract. Mech. , 55 : 443
- Ouyang , CS , Landis , E and Shah , SP . 1991 . J. Eng. Mech. – ASCE , 117 : 2681
- Harris , B , Habib , F and Cooke , R . 1992 . Proc. R. Soc. London A , 437 : 1899
- Mummery , PM , Derby , B and Scruby , CB . 1993 . Acta Metall. Mater. , 41 : 1431
- Barre , S and Benzeggagh , ML . 1994 . Compos. Sci. Techn. , 52 : 369
- de Groot , PJ , Wijnen , PAM and Janssen , RBF . 1995 . Compos. Sci. Techn. , 55 : 405
- Bohse , J . 2000 . Compos. Sci. Techn. , 60 : 1213
- Dzenis , YA and Saunders , I . 2002 . Int. J. Fract. , 117 : L23
- Petri , A , Paparo , G , Vespignani , A , Alippi , A and Costantini , M . 1994 . Phys. Rev. Lett. , 73 : 3423
- Garcimartin , A , Guarino , A , Bellon , L and Ciliberto , S . 1997 . Phys. Rev. Lett. , 79 : 3202
- Guarino , A , Garcimartin , A and Ciliberto , S . 1998 . Eur. Phys. J. B , 6 : 13
- Maes , C , van Moffaert , A , Frederix , H and Strauven , H . 1998 . Phys. Rev. B , 57 : 4987
- Guarino , A , Ciliberto , S , Garcimartin , A , Zei , M and Scorretti , R . 2002 . Eur. Phys. J. B , 26 : 141
- Salminen , LI , Tolvanen , AI and Alava , MJ . 2002 . Phys. Rev. Lett. , 89 : 185503
- Salminen , LI , Pulakka , JM , Rosti , J , Alava , MJ and Niskanen , KJ . 2006 . Europhys. Lett. , 73 : 55
- Amitrano , D . 2003 . J. Geophys. Res. B: Solid Earth , 108 : 2044
- Main , IG . 1991 . Geophys. J. Int. , 107 : 353
- Main , IG . 1992 . Geophys. J. Int. , 111 : 531
- Hatton , CG , Main , IG and Meredith , PG . 1993 . J. Struct. Geol. , 15 : 1485
- Main , IG , Sammonds , PR and Meredith , PG . 1993 . Geophys. J. Int. , 115 : 367
- Reches , Z and Lockner , DA . 1994 . J. Geophys. Res. B: Solid Earth , 99 : 18159
- Lyakhovsky , V , Ben-Zion , Y and Agnon , A . 1997 . J. Geophys. Res. B: Solid Earth , 102 : 27635
- Main , IG . 2000 . Geophys. J. Int. , 142 : 151
- Lei , XL , Kusunose , K , Nishizawa , O , Cho , A and Satoh , T . 2000 . Geophys. Res. Lett. , 27 : 1997
- Colombo , IS , Main , IG and Forde , MC . 2003 . J. Mat. Civ. Eng. , 15 : 280
- Aue , J and Hosson , JTMD . 1998 . J. Mat. Sci. , 33 : 5455
- Weiss , J and Marsan , D . 2003 . Science , 299 : 89
- Krysac , LC and Maynard , JD . 1998 . Phys. Rev. Lett. , 81 : 4428
- Lockner , DA , Byerlee , JD , Kuksenko , V , Ponomarev , A and Sidorin , A . 1991 . Nature , 350 : 39
- Shah , KR and Labuz , JF . 1995 . J. Geophys. Res. B: Solid Earth , 100 : 15527
- Labuz , JF and Biolzi , L . 1998 . Int. J. Sol. Struct. , 45 : 4191
- Zang , AR , Wagner , FC , Stanchits , S , Dresen , G , Andresen , R and Haidekker , MA . 1998 . Geophys. J. Int. , 135 : 1113
- Feng , XT and Seto , M . 1999 . Geophys. J. Int. , 136 : 275
- Hayakawa , K , Nakamura , T , Yonezawa , H and Tanaka , S . 2004 . Mater. Transac. , 45 : 3136
- Zietlow , WK and Labuz , JF . 1998 . Int. J. Rock Mech. Min. Sci. , 35 : 291
- Kanit , T , Forest , S , Galliet , I , Mounoury , V and Jeulin , D . 2003 . Int. J. Sol. Struct. , 40 : 3647
- Balankin , AS , Susarrey , O and Bravo , A . 2001 . Phys. Rev. E , 64 : 066131
- Rosti , J and Alava , MJ . 2006 . in press
- Anifrani , JC , Floch , CL , Sornette , D and Souillard , B . 1995 . J. Phys. I France , 5 : 631
- Johansen , A and Sornette , D . 2000 . Eur. Phys. J. B , 28 : 163
- Suresh , S . 1998 . Fatigue of Materials , Cambridge : Cambridge University Press .
- Santucci , S , Vanel , L and Ciliberto , S . 2004 . Phys. Rev. Lett. , 93 : 095505
- Nechad , H , Helmstetter , A , Guerouma , RE and Sornette , D . 2005 . Phys. Rev. Lett. , 94 : 045501
- Zaiser , M . 2006 . Adv. Phys. , 55 : 185
- Hähner , P , Ziegenbein , A , Rizzi , E and Neuhäuser , H . 2002 . Phys. Rev. B , 65 : 134109
- Deshpande , VS , Needleman , A and van der Giessen , E . 2001 . Scripta Mat. , 45 : 1047
- Nemat-Nasser , S . 1999 . Mech. Mater. , 31 : 493
- Needleman , A and Tvergaard , V . 2000 . Int. J. Fract. , 101 : 73
- Mahnken , R . 2002 . Int. J. Plasticity , 18 : 801
- Bazant , ZP , Rajapakse , Y , Allen , DH , Ballarini , R , Espinosa , HD , Gao , H , Gettu , R , Jirasek , M , Pijauder-Cabot , G Planas , J . 2002 . Int. J. Fract. , 113 : 345
- Clayton , JD and McDowell , DL . 2004 . Mech. Mater. , 36 : 799
- Ostoja-Starzewski , M . 2005 . Int. J. Plasticity , 21 : 1119
- Baret , JC , Vandembroucq , D and Roux , S . 2002 . Phys. Rev. Lett. , 89 : 195506
- Kahng , B , Batrouni , GG , Redner , S , de Arcangelis , L and Herrmann , HJ . 1988 . Phys. Rev. B , 37 : 7625
- Hansen , A , Hinrichsen , EL and Roux , S . 1991 . Phys. Rev. B , 43 : 665
- Ootani , I , Ohashi , Y , Ohashi , K and Fukuchi , M . 1992 . J. Phys. Soc. Jpn. , 61 : 1399
- Hristopulos , D and Uesaka , T . 2004 . Phys. Rev. E , 70 : 064108
- Chen , SH and Wang , TC . 2002 . Acta Mech. , 157 : 113
- Bolander , JE and Sukumar , N . 2005 . Phys. Rev. B , 71 : 094106
- Alava , M , Duxbury , PM , Moukarzel , C and Rieger , H . 2000 . Phase Transitions and Critical Phenomena , Edited by: Domb , C and Lebowitz , JL . Vol. 18 , New York : Academic Press .
- Kardar , M , Parisi , G and Zhang , YC . 1986 . Phys.Rev.Lett. , 56 : 889
- Alava , MJ , Karttunen , MEJ and Niskanen , KJ . 1995 . Europhys. Lett. , 32 : 142
- Li , YS and Duxbury , PM . 1988 . Phys. Rev. B , 38 : 9257
- Zapperi , S , Vespignani , A and Stanley , HE . 1997 . Nature , 388 : 658
- Nukala , PKVV and Simunovic , S . 2005 . Phys. Rev. E , 72 : 041919
- Otomar , DR , Menezes-Sobrinho , IL and Couto , MS . 2006 . Phys. Rev. Lett. , 96 : 095501
- Lamaignere , L , Carmona , F and Sornette , D . 1996 . Phys. Rev. Lett. , 77 : 2738
- Hansen , A , Roux , S and Herrmann , HJ . 1989 . J. Phys. , 50 : 733
- Arbabi , S and Sahimi , M . 1993 . Phys. Rev. B , 47 : 695
- Sahimi , M and Arbabi , S . 1993 . Phys. Rev. B , 47 : 703
- Nukala , PKVV , Zapperi , S and Simunovic , S . 2005 . Phys. Rev. E , 71 : 066106
- Feng , S and Sen , PN . 1984 . Phys. Rev. Lett. , 52 : 216
- Hassold , GN and Srolovitz , DJ . 1989 . Phys. Rev. B , 39 : 9273
- Roux , S and Guyon , E . 1985 . J. Phys. Lett. , 46 : L999
- Herrmann , HJ , Hansen , A and Roux , S . 1989 . Phys. Rev. B , 39 : 637
- Nukala , PKVV , Simunovic , S and Guddati , MN . 2005 . Int. J. Numer. Meth. Eng. , 62 : 1982
- Kantor , Y and Webman , I . 1984 . Phys. Rev. Lett. , 52 : 1891
- Sahimi , M and Goddard , JD . 1986 . Phys. Rev. B , 33 : 7848
- Monette , L and Anderson , MP . 1994 . Modelling Simul. Mater. Sci. Eng. , 2 : 53
- Xu , XP , Needleman , A and Abraham , FF . 1997 . Modelling Simul. Mater. Sci. Eng. , 5 : 489
- Xuan , W , Curtin , WA and Needleman , A . 2003 . Eng. Fract. Mech. , 70 : 1869
- Tomar , V , Zhai , J and Zhou , M . 2004 . Inter. J. Numer. Meth. Eng. , 61 : 1894
- Tomar , V and Zhou , M . 2005 . Eng. Fract. Mech. , 72 : 1920
- Chung , JW , Hosson , JTMD and vander Giessen , E . 2001 . Phys. Rev. B , 64 : 064202
- Chung , JW and Hosson , JTMD . 2002 . Phys. Rev. B , 66 : 064206
- Chung , JW , Hosson , JTMD and vander Giessen , E . 2002 . Phys. Rev. B , 65 : 094104
- Kunin , IA . 1982 . Elastic Media with Microstructure I , Berlin, , Germany : Springer-Verlag .
- Dai , H and Frantziskonis , G . 1994 . Mech. Mater. , 18 : 103
- Frantziskonis , GN , Konstantinidis , AA and Aifantis , EC . 2001 . European J. Mech. A/Sol. , 20 : 925
- Budiansky , B and O'Connell , RJ . 1976 . Int. J. Sol. Struct. , 12 : 81
- Belytschko , T and Black , T . 1999 . Inter. J. Numer. Meth. Eng. , 45 : 601
- Hillerborg , A , Modeer , M and Petersson , PE . 1976 . Cement Concrete Res. , 6 : 773
- de Borst , R , Sluys , LJ , Muhlhaus , H-B and Pamin , J . 1993 . Eng. Comput. , 10 : 99
- Pijaudier-Cabot , G and Bazant , ZP . 1988 . ASCE J. Eng. Mech. , 113 : 1512
- Peerlings , R , de Borst , R , Brekelmans , WAM and Geers , MGD . 1996 . Inter. J. Numer. Meth. Eng. , 39 : 3391
- Gutierrez , MA and de Borst , R . 1999 . Inter. J. Numer. Meth. Eng. , 44 : 1823
- Oliver , J . 1996 . Inter. J. Numer. Meth. Eng. , 39 : 3601
- Wells , GN and Sluys , LJ . 2001 . Inter. J. Numer. Meth. Eng. , 50 : 2667
- Simo , JC and Rifai , MS . 1990 . Inter. J. Numer. Meth. Eng. , 29 : 1595
- Daux , C , Moes , N , Dolbow , J , Sukumar , N and Belytschko , T . 2000 . Inter. J. Numer. Meth. Eng. , 45 : 1741
- Malenk , JM and Babuska , I . 1996 . Comp. Meth. App. Mech. Eng. , 39 : 289
- Sukumar , N and Prevost , JH . 2003 . Inter. J. Numer. Meth. Eng. , 40 : 7513
- Budyn , E , Zi , G , Moes , N and Belytschko , T . 2004 . Inter. J. Numer. Meth. Eng. , 61 : 1741
- Cafiero , R , Gabrielli , A , Marsili , M , Pietronero , L and Torosantucci , L . 1997 . Phys. Rev. Lett. , 79 : 1503
- Caldarelli , G , Cafiero , R and Gabrielli , A . 1998 . Phys. Rev. E , 57 : 3878
- Curtin , WA . 1991 . J. Am. Ceram. Soc. , 74 : 2837
- Curtin , WA and Scher , H . 1991 . Phys. Rev. Lett. , 67 : 2457
- Curtin , WA and Scher , H . 1992 . Phys. Rev. B , 45 : 2620
- Curtin , WA . 1993 . J. Mech. Phys. Sol. , 41 : 217
- Roux , S , Hansen , A and Hinrichsen , EL . 1993 . Phys. Rev. Lett. , 70 : 100
- Curtin , WA and Scher , H . 1993 . Phys. Rev. Lett. , 70 : 101
- Curtin , WA and Scher , H . 1993 . Phys. Rev. Lett. , 70 : 519
- Curtin , WA and Scher , H . 1997 . Phys. Rev. B , 55 : 12038
- Curtin , WA , Pamel , M and Scher , H . 1997 . Phys. Rev. B , 55 : 12051
- Sornette , D and Vanneste , C . 1992 . Phys. Rev. Lett. , 68 : 612
- Minozzi , M , Caldarelli , G , Pietronero , L and Zapperi , S . 2003 . Eur. Phys. J. B , 36 : 203
- Vlastos , S , Liu , E , Main , IG and Li , X.-Y . 2003 . Geophys. J. Int. , 152 : 649
- Bouchaud , E , Bouchaud , J.-P , Fisher , DS , Ramanathan , S and Rice , JR . 2000 . J. Mech. Phys. Sol. , 50 : 1703
- Ramanathan , S , Ertas , D and Fisher , DS . 1997 . Phys. Rev. Lett. , 79 : 873
- Cox , BN , Gao , H , Gross , D and Rittel , D . 2005 . J. Mech. Phys. Sol. , 53 : 565
- Marder , M and Liu , X . 1993 . Phys. Rev. Lett. , 71 : 2417
- Karma , A , Kessler , D and Levine , H . 2001 . Phys. Rev. Lett. , 87 : 045501
- Aranson , IS , Kalatsky , VA and Vinokur , VM . 2000 . Phys. Rev. Lett. , 85 : 118
- Eastgate , LO , Sethna , JP , Rauscher , M , Cretegny , T , Chen , CS and Myers , CR . 2002 . Phys. Rev. E , 65 : 036117
- Karma , A and Lobkovsky , AE . 2004 . Phys. Rev. Lett. , 92 : 245510
- Rautiainen , TT , Alava , MJ and Kaski , K . 1995 . Phys. Rev. E , 51 : R2727
- Heino , P and Kaski , K . 1996 . Phys. Rev. B , 54 : 6150
- Heino , P and Kaski , K . 1997 . Phys. Rev. E , 56 : 4364
- Moriarty , JA , Belak , JF , Rudd , RE , Soderlind , P , Streitz , FH and Yang , LH . 2002 . J. Phys.: Condens. Matter , 14 : 2825
- Selinger , RLB , Wang , Z.-G , Gelbart , WM and Ben-Saul , A . 1991 . Phys. Rev. A , 43 : 4396
- Selinger , RLB , Wang , Z.-G and Gelbart , WM . 1991 . J. Chem. Phys. , 95 : 9128
- Wang , Z.-G , Landman , U , Selinger , RLB and Gelbart , WM . 1991 . Phys. Rev. B , 44 : 378
- Abraham , FF , Wallup , R , Gao , H , Duchelneau , M , la Rubia , TDD and Seager , M . 2002 . PNAS , 99 : 5777
- Lorentz , CD and Stevens , MJ . 2003 . Phys. Rev. E , 68 : 021802
- Buxton , GA and Balazs , AC . 2004 . Phys. Rev. B , 69 : 054101
- Seppala , E , Belak , J and Rudd , R . 2004 . Phys. Rev. Lett. , 93 : 245503
- Kalia , RK , Nakano , A , Omeltchenko , A , Tsuruta , K and Vashishta , P . 1997 . Phys. Rev. Lett. , 78 : 2144
- Rountree , CL , Kalia , RK , Lidorikis , E , Nakano , A , Brutzel , LV and Vashishta , P . 2002 . Ann. Rev. Mater. Res. , 32 : 377
- Kalia , RK , Nakano , A , Vashishta , P , Rountree , CL , van Brutzel , L and Ogata , S . 2003 . Int. J. Fract. , 121 : 71
- Lu , Q and Bhattacharya , B . 2005 . Eng. Fract. Mech. , 72 : 2037
- Hemmer , PC and Hansen , A . 1992 . J. Appl. Mech. , 59 : 909
- Hansen , A and Hemmer , PC . 1994 . Phys. Lett. A , 184 : 394
- Sornette , D . 1992 . J. Phys. I France , 2 : 2089
- Kloster , PM , Hemmer , C and Hansen , A . 1997 . Phys. Rev. E , 56 : 2615
- Harlow , DG and Phoenix , SL . 1978 . J. Compos. Mater. , 12 : 195
- Smith , RL . 1980 . Proc. R. Soc. London A , 372 : 179
- Smith , RL and Phoenix , SL . 1981 . J. Appl. Mech. , 48 : 75
- Beyerlein , IJ and Phoenix , SL . 1996 . J. Mech. Phys. Sol. , 44 : 1997
- Phoenix , SL , Ibnabdeljalil , M and Hui , C-Y . 1997 . Int. J. Sol. Struct. , 34 : 545
- Phoenix , SL and Ra , R . 1992 . Acta Metall. Mater. , 40 : 2813
- Zhou , SJ and Curtin , WA . 1995 . Acta. Metall. Mater. , 43 : 3093
- Leath , PL and Duxbury , PM . 1994 . Phys. Rev. B , 49 : 14905
- Zhang , S and Ding , E . 1996 . Phys. Rev. B , 53 : 646
- Krajcinovic , D and Silva , MAG . 1982 . Int. J. Sol. Struct. , 18 : 551
- Fabeny , B and Curtin , WA . 1996 . Acta Mater. , 44 : 3439
- Hidalgo , RC , Kun , F and Herrmann , HJ . 2002 . Phys. Rev. E , 65 : 032502
- Kun , F , Hidalgo , RC , Herrmann , HJ and Pál , KF . 2003 . Phys. Rev. E , 67 : 061802
- Kun , F , Zapperi , S and Herrmann , HJ . 2000 . Eur. Phys. J. B , 17 : 269
- Raischel , F , Kun , F and Herrmann , HJ . 2006 . cond-mat/0601290 ,
- Roux , S . 2000 . Phys. Rev. E , 62 : 6164
- Scorretti , R , Ciliberto , S and Guarino , A . 2001 . Europhys. Lett. , 55 : 626
- Politi , A , Ciliberto , S and Scorretti , R . 2002 . Phys. Rev. E , 66 : 026107
- da Silveira , R . 1998 . Phys. Rev. Lett. , 80 : 3157
- Pradhan , S , Hansen , A and Hemmer , PC . 2005 . Phys. Rev. Lett. , 95 : 125501
- Mahesh , S and Phoenix , SL . 2004 . Phys. Rev. E , 69 : 026102
- Hidalgo , RC , Moreno , Y , Kun , F and Herrmann , HJ . 2002 . Phys. Rev. E , 65 : 046148
- Pradhan , S , Chakrabarti , BK and Hansen , A . 2005 . Phys. Rev. E , 71 : 036149
- Sethna , JP , Dahmen , K , Kartha , S , Krumhansl , JA , J , Roberts , BW and Shore , D . 1993 . Phys. Rev. Lett. , 70 : 3347
- Dahmen , K and Sethna , JP . 1996 . Phys. Rev. B , 53 : 14872
- Sethna , J , Dahmen , KA and Myers , CR . 2001 . Nature , 410 : 242
- Rundle , JB and Klein , W . 1989 . Phys. Rev. Lett. , 63 : 171
- Golubovic , L and Feng , S . 1991 . Phys. Rev. A , 43 : 5223
- Golubovic , L and Pedrera , A . 1995 . Phys. Rev. E , 51 : 2799
- Buchel , A and Sethna , JP . 1997 . Phys. Rev. E , 55 : 7669
- Zapperi , S , Ray , P , Stanley , HE and Vespignani , A . 1997 . Phys. Rev. Lett. , 78 : 1408
- Zapperi , S , Ray , P , Stanley , HE and Vespignani , A . 1999 . Phys. Rev. E , 59 : 5049
- Andersen , JV , Sornette , D and Leung , KW . 1997 . Phys. Rev. Lett. , 78 : 2140
- Barthelemy , M , da Silveira , R and Orland , H . 2002 . Europhys. Lett. , 57 : 831
- Toussaint , R and Pride , SR . 2005 . Phys. Rev. E , 71 : 046127
- Schmittbuhl , J , Roux , S , Villotte , JP and Maloy , KJ . 1995 . Phys. Rev. Lett. , 74 : 1787
- Ramanathan , S and Fisher , DS . 1997 . Phys. Rev. Lett. , 79 : 877
- Ramanathan , S and Fisher , DS . 1998 . Phys. Rev. B , 58 : 6026
- Gao , H and Rice , JR . 1989 . J. Appl. Mech. , 56 : 828
- Ertas , D and Kardar , M . 1994 . Phys. Rev. E , 49 : R2532
- Rosso , A and Krauth , W . 2002 . Phys. Rev. E , 65 : 025101
- Schmittbuhl , J and Villotte , JP . 1999 . Physica A , 270 : 42
- Zapperi , S , Herrmann , HJ and Roux , S . 2000 . Eur. Phys. J. B , 17 : 131
- Aström , JA , Alava , MJ and Timonen , J . 2000 . Phys. Rev. E , 62 : 2878
- Schmittbuhl , J , Hansen , A and Batrouni , GG . 2003 . Phys. Rev. Lett. , 90 : 045505
- Bouchbinder , E , Mathiesen , J and Procaccia , I . 2004 . Phys. Rev. Lett. , 92 : 245505
- Doussal , PL , Wiese , KJ , Raphael , E and Golestanian , R . 2004 . cond-mat/0411652 ,
- Rosso , A , Hartmann , AK and Krauth , W . 2003 . Phys. Rev. E , 67 : 021602
- Tang , LH and Leshhorn , H . 1992 . Phys. Rev. A , 45 : R8309
- Buldyrev , SV , Barabasi , A.-L , Caserta , F , Havlin , S , Stanley , HE and Vicsek , T . 1992 . 45 : R8313
- Prades , S , Bonamy , D , Dalmas , D , Bouchaud , E and Guillot , C . 2004 . Int. J. Sol. Struct. , 42 : 637
- Stauffer , D and Aharony , A . 1994 . Introduction to Percolation Theory, , Revised 2nd ed , Philadelphia, , USA : Taylor and Francis .
- Grassberger , P . 1999 . Physica A , 262 : 251
- Clerc , JP , Podolskiy , VA and Sarychev , AK . 2000 . Eur. Phys. J. B , 15 : 507
- Moukarzel , C , Duxbury , PM and Leath , PL . 1997 . Phys. Rev. Lett. , 78 : 1480
- Feng , S , Halperin , BI and Sen , PN . 1987 . Phys. Rev. B , 35 : 1897
- Stenull , O and Janssen , HK . 2001 . Phys. Rev. E , 64 : 056105
- Alava , MJ and Moukarzel , CF . 2003 . Phys. Rev. E , 67 : 056106
- Roux , S , Hansen , A , Herrmann , HJ and Guyon , E . 1988 . J. Stat. Phys. , 52 : 237
- Moukarzel , CF . 1998 . Int. J. Mod. Phys. C , 9 : 887
- Duxbury , PM , Leath , PL and Beale , PD . 1987 . Phys. Rev. B , 36 : 367
- Duxbury , PM , Beale , PD and Leath , PL . 1986 . Phys. Rev. Lett. , 57 : 1052
- Gumbel , EJ . 2004 . Statistics of Extremes , New York : Columbia University Press .
- Sapoval , B , Rosso , M and Gouyet , JF . 1985 . J. Phys. Lett. (Paris) , 46 : L149
- Baldassarri , A , Gabrielli , G and Sapoval , B . 2002 . Europhys. Lett. , 59 : 232
- Schmittbuhl , J , Hansen , A and Batrouni , GG . 2004 . Phys. Rev. Lett. , 92 : 049602
- Alava , MJ and Zapperi , S . 2004 . Phys. Rev. Lett. , 92 : 049601
- Asikainen , J , Majaniemi , S , Dubé , M and Nissila , TA . 2002 . Phys. Rev. E , 65 : 052104
- Hansen , A and Schmittbuhl , J . 2003 . Phys. Rev. Lett. , 90 : 045504
- Nukala , PKVV , Simunovic , S and Zapperi , S . 2004 . J. Stat. Mech. , : P08001
- de Arcangelis , L , Hansen , A , Herrmann , HJ and Roux , S . 1989 . Phys. Rev. B , 40 : 877
- Krajcinovic , D and Rinaldi , A . 2005 . J. Appl. Mech. , 72 : 76
- Sahimi , M and Arbabi , S . 1993 . Phys. Rev. B , 47 : 713
- Sahimi , M . 1998 . Phy. Reports , 306 : 213
- Arbabi , S and Sahimi , M . 1990 . Phys. Rev. B , 41 : 772
- Delaplace , A , Pijaudier-Cabot , G and Roux , S . 1996 . J. Mech. Phys. Sol. , 44 : 99
- de Arcangelis , L and Herrmann , HJ . 1989 . Phys. Rev. B , 39 : 2678
- Reurings , F and Alava , MJ . 2005 . Eur. Phys. J. B , 47 : 85
- Zapperi , S and Nukala , PKVV . 2006 . Int. J. Fract , in press
- Räisänen , VI , Seppala , ET , Alava , MJ and Duxbury , PM . 1998 . Phys. Rev. Lett. , 80 : 329
- Ramstad , T , Bakke , JH , Bjelland , J , Stranden , T and Hansen , A . 2004 . Phys. Rev. E , 70 : 036123
- Bakke , JOH , Bjelland , J , Ramstad , T , Stranden , T , Hansen , A and Schmittbuhl , J . 2003 . Phys. Scripta , T106 : 65
- Nukala , PKVV , Zapperi , S and Simunovic , S . 2006 . unpublished
- Duxbury , PM and Leath , PL . 1994 . Phys. Rev. Lett. , 72 : 2805
- Duxbury , PM , Kim , SG and Leath , PL . 1994 . Mater. Sci. Eng. A , 176 : 25
- Nukala , S , Nukala , PKVV , Simunovic , S and Guess , F . 2006 . Phys. Rev. E , 71 : 036109
- Smalley , RF , Turcotte , DL and Solla , SA . 1985 . J. Geophys. Res. , 90 : 1894
- Newman , WI and Gabrielov , AM . 1991 . Int. J. Fract. , 50 : 1
- Newman , WI , Gabrielov , AM , Durand , TA , Phoenix , SL and Turcotte , DL . 1994 . Physica D , 77 : 200
- Beale , PD and Srolovitz , DJ . 1988 . Phys. Rev. B , 37 : 5500
- Nukala , PKVV and Simunovic , S . 2004 . Eur. Phys. J. B , 37 : 91
- Seppälä , ET , Räisänen , VI and Alava , MJ . 2000 . Phys. Rev. E , 61 : 6312
- Bazant , ZP and Yavari , A . 2005 . Eng. Fract. Mech. , 72 : 1
- Hansen , A , Hinrichsen , EL and Roux , S . 1991 . Phys. Rev. Lett. , 66 : 2476
- Zapperi , S , Nukala , PKVV and Simunovic , S . 2005 . Phys. Rev. E , 71 : 026106
- Batrouni , GG and Hansen , A . 1998 . Phys. Rev. Lett. , 80 : 325
- Räisänen , VI , Alava , MJ and Nieminen , RM . 1998 . Phys. Rev. B , 58 : 14288
- Skjetne , B , Helle , T and Hansen , A . 2001 . Phys. Rev. Lett. , 87 : 125503
- Parisi , A , Caldarelli , G and Pietronero , L . 2000 . Europhys. Lett. , 52 : 304
- Foltin , G , Oerding , K , Rácz , Z , Workman , RL and Zia , RKP . 1994 . Phys. Rev. E , 50 : R639
- Rosso , A , Krauth , W , Doussal , PL , Vannimenus , J and Wiese , KJ . 2003 . Phys. Rev. E , 68 : 036128
- Zapperi , S , Nukala , PKVV and Simunovic , S . 2005 . Physica A , 357 : 129
- Meacci , G , Politi , A and Zei , M . 2004 . Europhys. Lett. , 66 : 55
- Caldarelli , G , Castellano , C and Petri , A . 1999 . Phil. Mag. B , 79 : 1939
- Caldarelli , G , di Tolla , F and Petri , A . 1996 . Phys. Rev. Lett. , 77 : 2503
- Andersen , J and Sornette , D . 2005 . cond-mat/0508549 ,
- Barrett , R , Berry , M , Chan , TF , Demmel , J , Donato , J , Dongarra , J , Eijkhout , V , Pozo , R , Romine , C and der Vorst , HV . 1994 . Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, , 2nd , Philadelphia : SIAM .
- Briggs , WL , Henson , VE and McCormick , SF . 2000 . A Multigrid Tutorial, , 2nd , Philadelphia : SIAM .
- Batrouni , GG , Hansen , A and Nelkin , M . 1986 . Phys. Rev. Lett. , 57 : 1336
- Batrouni , GG and Hansen , A . 1988 . J. Stat. Phys. , 52 : 747
- Luenberger , DG . 1984 . Linear and Nonlinear Programming, , 2nd , Reading : Addison-Wesley Publishing Company .
- O‘Shaughnessy and Procaccia , I . 1985 . Phys. Rev. Lett. , 54 : 455
- O‘Shaughnessy and Procaccia , I . 1985 . Phys. Rev. A , 32 : 3073
- Chan , T . 1988 . SIAM J. Sci. Stat. Comput. , 9 : 766
- Chan , RH . 1989 . SIAM J. Matrix Anal. Appl. , 10 : 542
- Chan , R and Chan , T . 1992 . Numer. Linear Alg. Appl. , 1 : 77
- Chan , RH and Ng , MK . 1996 . SIAM Rev. , 38 : 427
- Tyrtyshnikov , E . 1992 . SIAM J. Matrix Anal. Appl. , 13 : 459
- Golub , GH and van Loan , CF . 1996 . Matrix Computations , Baltimore : The Johns Hopkins University Press .
- Gupta , A , Joshi , M and Kumar , V . 2001 . Technical Report RC 22038 (98932) , Yorktown Heights, NY : IBM T.J. Watson Research Center .
- Amestoy , PR , Duff , IS , L‘Excellent , J-Y and Koster , J . 2001 . SIAM J. Matrix Anal. Appl. , 23 : 15
- Toledo , S , Chen , D and Rotkin , V . 2001 . http://www.tau.ac.il/stoledo/taucs/
- Nukala , PKVV and Simunovic , S . 2003 . J. Phys. A: Math. Gen. , 36 : 11403
- Davis , TA and Hager , WW . 1999 . SIAM J. Matrix Anal. Appl. , 20 : 606
- Davis , TA and Hager , WW . 2001 . SIAM J. Matrix Anal. Appl. , 22 : 997
- Nukala , PKVV and Simunovic , S . 2004 . J. Phys. A: Math. Gen. , 37 : 2093