1932

Abstract

We give a bird's-eye view of the plastic deformation of crystals aimed at the statistical physics community, as well as a broad introduction to the statistical theories of forced rigid systems aimed at the plasticity community. Memory effects in magnets, spin glasses, charge density waves, and dilute colloidal suspensions are discussed in relation to the onset of plastic yielding in crystals. Dislocation avalanches and complex dislocation tangles are discussed via a brief introduction to the renormalization group and scaling. Analogies to emergent scale invariance in fracture, jamming, coarsening, and a variety of depinning transitions are explored. Dislocation dynamics in crystals challenge nonequilibrium statistical physics. Statistical physics provides both cautionary tales of subtle memory effects in nonequilibrium systems and systematic tools designed to address complex scale-invariant behavior on multiple length scales and timescales.

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2017-07-03
2024-04-24
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Literature Cited

  1. Chandler D. 1.  1987. Introduction to Modern Statistical Mechanics Oxford, UK: Oxford Univ. Press
  2. Forster D. 2.  1995. Hydrodynamic Fluctuations, Broken Symmetry, and Correlation Functions Reading, MA: Perseus Books
  3. Martin PC. 3.  1968. Problème à N corps (Many Body Physics) New York: Gordon and Breach
  4. Landau L, Lifshitz E. 4.  2013. Statistical Physics Oxford, UK: Elsevier Sci.
  5. Tadmor EB, Miller RE, Elliott RS. 5.  2012. Continuum Mechanics and Thermodynamics: From Fundamental Concepts to Governing Equations Cambridge, UK: Cambridge Univ. Press
  6. Anderson PW. 6.  1978. Lectures on amorphous systems. Les Houches Session XXXI R Balian, R Maynard, G Toulouse, pp. 158–261 Singapore: World Sci. [Google Scholar]
  7. Sethna JP. 7.  2006. Statistical Mechanics: Entropy, Order Parameters, and Complexity http://www.physics.cornell.edu/sethna/StatMech/ Oxford, UK: Oxford Univ. Press
  8. Chui ST, Weeks JD. 8.  1978. Dynamics of the roughening transition. Phys. Rev. Lett. 40:733–36 [Google Scholar]
  9. Liarte DB, Bierbaum M, Mosna RA, Kamien RD, Sethna JP. 9.  2016. Weirdest martensite: smectic liquid crystal microstructure and Weyl-Poincaré invariance. Phys. Rev. Lett. 116:147802 [Google Scholar]
  10. Vegge T, Sethna JP, Cheong SA, Jacobsen KW, Myers CR, Ralph DC. 10.  2001. Calculation of quantum tunneling for a spatially extended defect: The dislocation kink in copper has a low effective mass. Phys. Rev. Lett. 86:1546–49 [Google Scholar]
  11. Hull D, Bacon DJ. 11.  2011. Introduction to Dislocations Oxford, UK: Elsevier
  12. Bulatov VV, Hsiung LL, Tang M, Arsenlis A, Bartelt MC. 12.  et al. 2006. Dislocation multi-junctions and strain hardening. Nature 440:1174–78 [Google Scholar]
  13. Taylor GI. 13.  1934. The mechanism of plastic deformation of crystals. I. Theoretical. Proc. R. Soc. Ser. A Math. Phys. Eng. Sci. 145:362–87 [Google Scholar]
  14. Budrikis Z, Zapperi S. 14.  2013. Avalanche localization and crossover scaling in amorphous plasticity. Phys. Rev. E 88:062403 [Google Scholar]
  15. Sandfeld S, Budrikis Z, Zapperi S, Castellanos DF. 15.  2015. Avalanches, loading and finite size effects in 2D amorphous plasticity: results from a finite element model. J. Stat. Mech. Theory Exp. 2015:P02011 [Google Scholar]
  16. Dieter GE, Bacon DJ. 16.  1986. Mechanical Metallurgy New York: McGraw-Hill
  17. Bi D, Henkes S, Daniels KE, Chakraborty B. 17.  2015. The statistical physics of athermal materials. Annu. Rev. Condens. Matter Phys. 6:63–83 [Google Scholar]
  18. Edwards S, Oakeshott R. 18.  1989. Theory of powders. Physica A Stat. Mech. Appl. 157:1080–90 [Google Scholar]
  19. Martiniani S, Schrenk KJ, Ramola K, Chakraborty B, Frenkel D. 19.  2016. Are some packings more equal than others? A direct test of the Edwards conjecture. arXiv:1610.06328 [cond-mat.soft]
  20. Henkes S, Chakraborty B. 20.  2005. Jamming as a critical phenomenon: a field theory of zero-temperature grain packings. Phys. Rev. Lett. 95:198002 [Google Scholar]
  21. Edwards S. 21.  2005. The full canonical ensemble of a granular system. Physica A Stat. Mech. Appl. 353:114–18 [Google Scholar]
  22. Blumenfeld R, Edwards S. 22.  2009. On granular stress statistics: compactivity, angoricity, and some open issues. J. Phys. Chem. B 113:3981–87 [Google Scholar]
  23. Jenkins JT. 23.  2015. Kinetic theories for collisional grain flows. Handbook of Granular Materials SV Franklin, MD Shattuck, pp. 155–86 Boca Raton, FL: CRC Press [Google Scholar]
  24. Puckett JG, Daniels KE. 24.  2013. Equilibrating temperaturelike variables in jammed granular subsystems. Phys. Rev. Lett. 110:058001 [Google Scholar]
  25. Langer J, Bouchbinder E, Lookman T. 25.  2010. Thermodynamic theory of dislocation-mediated plasticity. Acta Mater. 58:3718–32 [Google Scholar]
  26. Makse HA, Kurchan J. 26.  2002. Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment. Nature 415:614–17 [Google Scholar]
  27. Abate AR, Durian DJ. 27.  2008. Effective temperatures and activated dynamics for a two-dimensional air-driven granular system on two approaches to jamming. Phys. Rev. Lett. 101:245701 [Google Scholar]
  28. Berthier L, Barrat JL. 28.  2002. Shearing a glassy material: numerical tests of nonequilibrium mode-coupling approaches and experimental proposals. Phys. Rev. Lett. 89:095702 [Google Scholar]
  29. Ono IK, O'Hern CS, Durian DJ, Langer SA, Liu AJ, Nagel SR. 29.  2002. Effective temperatures of a driven system near jamming. Phys. Rev. Lett. 89:095703 [Google Scholar]
  30. Jonason K, Vincent E, Hammann J, Bouchaud J, Nordblad P. 30.  1998. Memory and chaos effects in spin glasses. Phys. Rev. Lett. 81:3243–46 [Google Scholar]
  31. Sethna JP, Dahmen K, Kartha S, Krumhansl JA, Roberts BW, Shore JD. 31.  1993. Hysteresis and hierarchies—dynamics of disorder-driven first-order phase transformations. Phys. Rev. Lett. 70:3347–50 [Google Scholar]
  32. Coppersmith S. 32.  1987. A simple illustration of phase organization. Phys. Lett. A 125:473–75 [Google Scholar]
  33. Coppersmith S, Littlewood P. 33.  1987. Pulse-duration memory effect and deformable charge-density waves. Phys. Rev. B 36:311–17 [Google Scholar]
  34. Tang C, Wiesenfeld K, Bak P, Coppersmith S, Littlewood P. 34.  1987. Phase organization. Phys. Rev. Lett. 58:1161–64 [Google Scholar]
  35. Asaro R, Lubarda V. 35.  2006. Mechanics of Solids and Materials Cambridge, UK: Cambridge Univ. Press
  36. de Silva CW. 36.  2013. Mechanics of Materials Boca Raton, FL: CRC Press
  37. Nair S. 37.  2015. Mechanics of Aero-Structures Cambridge, UK: Cambridge Univ. Press
  38. Philpot T. 38.  2012. Mechanics of Materials: An Integrated Learning System Hoboken, NJ: Wiley Glob. Educ., 3rd ed..
  39. Machta BB, Chachra R, Transtrum M, Sethna JP. 39.  2013. Parameter space compression underlies emergent theories and predictive models. Science 342:604–7 [Google Scholar]
  40. Transtrum MK, Machta BB, Brown KS, Daniels BC, Myers CR, Sethna JP. 40.  2015. Perspective: Sloppiness and emergent theories in physics, biology, and beyond. J. Chem. Phys. 143:010901 [Google Scholar]
  41. Kocks UF, Tomé CN, Wenk HR. 41.  2000. Texture and Anisotropy: Preferred Orientations in Polycrystals and Their Effect on Materials Properties Cambridge, UK: Cambridge Univ. Press
  42. Randle V, Engler O. 42.  2000. Introduction to Texture Analysis: Macrotexture, Microtexture and Orientation Mapping London: Gordon and Breach
  43. Bhattacharya K. 43.  2003. Microstructure of Martensite: Why It Forms and How It Gives Rise to the Shape-Memory Effect Oxford, UK: Oxford Univ. Press
  44. Corté L, Chaikin PM, Gollub JP, Pine DJ. 44.  2008. Random organization in periodically driven systems. Nat. Phys. 4:420–24 [Google Scholar]
  45. Pine D, Gollub J, Brady J, Leshansky A. 45.  2005. Chaos and threshold for irreversibility in sheared suspensions. Nature 438:997–1000 [Google Scholar]
  46. Paulsen JD, Keim NC, Nagel SR. 46.  2014. Multiple transient memories in experiments on sheared non-Brownian suspensions. Phys. Rev. Lett. 113:068301 [Google Scholar]
  47. Reichhardt C, Reichhardt CJO. 47.  2009. Random organization and plastic depinning. Phys. Rev. Lett. 103:168301 [Google Scholar]
  48. Keim NC, Arratia PE. 48.  2013. Yielding and microstructure in a 2D jammed material under shear deformation. Soft Matter 9:6222–25 [Google Scholar]
  49. Keim NC, Arratia PE. 49.  2014. Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material. Phys. Rev. Lett. 112:028302 [Google Scholar]
  50. Menon GI, Ramaswamy S. 50.  2009. Universality class of the reversible-irreversible transition in sheared suspensions. Phys. Rev. E 79:061108 [Google Scholar]
  51. Regev I, Weber J, Reichhardt C, Dahmen KA, Lookman T. 51.  2015. Reversibility and criticality in amorphous solids. Nat. Commun. 6:8805 [Google Scholar]
  52. Regev I, Lookman T, Reichhardt C. 52.  2013. Onset of irreversibility and chaos in amorphous solids under periodic shear. Phys. Rev. E 88:062401 [Google Scholar]
  53. Fiocco D, Foffi G, Sastry S. 53.  2013. Oscillatory athermal quasistatic deformation of a model glass. Phys. Rev. E 88:020301(R) [Google Scholar]
  54. Jeanneret R, Bartolo D. 54.  2014. Geometrically protected reversibility in hydrodynamic Loschmidt-echo experiments. Nat. Commun. 5:3474 [Google Scholar]
  55. Nagamanasa KH, Gokhale S, Sood AK, Ganapathy R. 55.  2014. Experimental signatures of a nonequilibrium phase transition governing the yielding of a soft glass. Phys. Rev. E 89:062308 [Google Scholar]
  56. Rogers MC, Chen K, Andrzejewski L, Narayanan S, Ramakrishnan S. 56.  et al. 2014. Echoes in X-ray speckles track nanometer-scale plastic events in colloidal gels under shear. Phys. Rev. E 90:062310 [Google Scholar]
  57. Möbius R, Heussinger C. 57.  2014. (Ir)reversibility in dense granular systems driven by oscillating forces. Soft Matter 10:4806–12 [Google Scholar]
  58. Schreck CF, Hoy RS, Shattuck MD, O'Hern CS. 58.  2013. Particle-scale reversibility in athermal particulate media below jamming. Phys. Rev. E 88:052205 [Google Scholar]
  59. Slotterback S. 59.  2012. Onset of irreversibility in cyclic shear of granular packings. Phys. Rev. E 85:021309 [Google Scholar]
  60. Royer JR, Chaikin PM. 60.  2015. Precisely cyclic sand: self-organization of periodically sheared frictional grains. PNAS 112:49–53 [Google Scholar]
  61. Zhou C, Olson Reichhardt C, Reichhardt C, Beyerlein I. 61.  2014. Random organization in periodically driven gliding dislocations. Phys. Lett. A 378:1675–78 [Google Scholar]
  62. Okuma S, Tsugawa Y, Motohashi A. 62.  2011. Transition from reversible to irreversible flow: absorbing and depinning transitions in a sheared-vortex system. Phys. Rev. B 83:012503 [Google Scholar]
  63. Mangan N, Reichhardt C, Olson Reichhardt CJ. 63.  2008. Reversible to irreversible flow transition in periodically driven vortices. Phys. Rev. Lett. 100:187002 [Google Scholar]
  64. Pérez Daroca D, Pasquini G, Lozano GS, Bekeris V. 64.  2011. Dynamics of superconducting vortices driven by oscillatory forces in the plastic-flow regime. Phys. Rev. B 84:012508 [Google Scholar]
  65. López D, Kwok WK, Safar H, Olsson RJ, Petrean AM. 65.  et al. 1999. Spatially resolved dynamic correlation in the vortex state of high temperature superconductors. Phys. Rev. Lett. 82:1277–80 [Google Scholar]
  66. Miguel MC, Zapperi S. 66.  2003. Tearing transition and plastic flow in superconducting thin films. Nat. Mater. 2:477–81 [Google Scholar]
  67. Shaw G, Mandal P, Banerjee SS, Niazi A, Rastogi AK. 67.  et al. 2012. Critical behavior at depinning of driven disordered vortex matter in 2H-NbS2. Phys. Rev. B 85:174517 [Google Scholar]
  68. Okuma S, Motohashi A. 68.  2012. Critical behavior associated with transient dynamics near the depinning transition. New J. Phys. 14:477 [Google Scholar]
  69. Goldenfeld N. 69.  1992. Lectures on Phase Transitions and the Renormalization Group Reading, MA: Addison-Wesley
  70. Sethna JP, Dahmen KA, Myers CR. 70.  2001. Crackling noise. Nature 410:242–50 [Google Scholar]
  71. Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S. 71.  2007. Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318:251–54 [Google Scholar]
  72. Friedman N, Jennings AT, Tsekenis G, Kim JY, Tao M. 72.  et al. 2012. Statistics of dislocation slip avalanches in nanosized single crystals show tuned critical behavior predicted by a simple mean field model. Phys. Rev. Lett. 109:095507 [Google Scholar]
  73. Burridge R, Knopoff L. 73.  1967. Model and theoretical seismicity. Bull. Seismol. Soc. Am. 57:341–71 [Google Scholar]
  74. Bak P, Tang C. 74.  1989. Earthquakes as a self-organized critical phenomenon. J. Geophys. Res. 94:635–15 [Google Scholar]
  75. Petri A, Paparo G, Vespignani A, Alippi A, Costantini M. 75.  1994. Experimental evidence for critical dynamics in microfracturing processes. Phys. Rev. Lett. 73:3423–26 [Google Scholar]
  76. Garcimartin A, Guarino A, Bellon L, Ciliberto S. 76.  1997. Statistical properties of fracture precursors. Phys. Rev. Lett. 79:3202–5 [Google Scholar]
  77. Chen Y, Papanikolaou S, Sethna JP, Zapperi S, Durin G. 77.  2011. Avalanche spatial structure and multivariable scaling functions; sizes, heights, widths, and views through windows. Phys. Rev. E 84:061103 [Google Scholar]
  78. Papanikolaou S, Bohn F, Sommer RL, Durin G, Zapperi S, Sethna JP. 78.  2011. Universality beyond power laws and the average avalanche shape. Nat. Phys. 7:316–20 [Google Scholar]
  79. Miguel MC, Vespignani A, Zapperi S, Weiss J, Grasso JR. 79.  2001. Intermittent dislocation flow in viscoplastic deformation. Nature 410:667–71 [Google Scholar]
  80. Dimiduk DM, Woodward C, LeSar R, Uchic MD. 80.  2006. Scale-free intermittent flow in crystal plasticity. Science 312:1188–90 [Google Scholar]
  81. Weiss J, Marsan D. 81.  2003. Three-dimensional mapping of dislocation avalanches: clustering and space/time coupling. Science 299:89–92 [Google Scholar]
  82. Mughrabi H. 82.  1983. Dislocation wall and cell structures and long-range internal stresses in deformed metal crystals. Acta Metall. 31:1367–79 [Google Scholar]
  83. Hähner P, Bay K, Zaiser M. 83.  1998. Fractal dislocation patterning during plastic deformation. Phys. Rev. Lett. 81:2470–73 [Google Scholar]
  84. Hughes D, Chrzan D, Liu Q, Hansen N. 84.  1998. Scaling of misorientation angle distributions. Phys. Rev. Lett. 81:4664–67 [Google Scholar]
  85. Chen YS, Choi W, Papanikolaou S, Bierbaum M, Sethna JP. 85.  2013. Scaling theory of continuum dislocation dynamics in three dimensions: self-organized fractal pattern formation. Int. J. Plast. 46:94–129 [Google Scholar]
  86. Chen YS, Choi W, Papanikolaou S, Sethna JP. 86.  2010. Bending crystals: the evolution of grain boundaries and fractal dislocation structures. Phys. Rev. Lett. 105:105501 [Google Scholar]
  87. Bertalan Z, Shekhawat A, Sethna JP, Zapperi S. 87.  2014. Fracture strength: stress concentration, extreme value statistics, and the fate of the Weibull distribution. Phys. Rev. Appl. 2:034008 [Google Scholar]
  88. Kent-Dobias J, Shekhawat A, Sethna JP. 88.  2016. Work in progress
  89. Alava MJ, Nukala PK, Zapperi S. 89.  2006. Morphology of two-dimensional fracture surfaces. J. Stat. Mech. Theory Exp. 2006:L10002 [Google Scholar]
  90. Zapperi S, Nukala PKV, Šimunović S. 90.  2005. Crack roughness and avalanche precursors in the random fuse model. Phys. Rev. E 71:026106 [Google Scholar]
  91. Alava MJ, Nukala PK, Zapperi S. 91.  2006. Statistical models of fracture. Adv. Phys. 55:349–476 [Google Scholar]
  92. Bouchaud E, Lapasset G, Planes J. 92.  1990. Fractal dimension of fractured surfaces: a universal value?. EPL 13:73 [Google Scholar]
  93. Bouchaud E. 93.  1997. Scaling properties of cracks. J. Phys. Condens. Matter 9:4319–44 [Google Scholar]
  94. Ponson L, Bonamy D, Bouchaud E. 94.  2006. Two-dimensional scaling properties of experimental fracture surfaces. Phys. Rev. Lett. 96:035506 [Google Scholar]
  95. Morel S, Schmittbuhl J, Bouchaud E, Valentin G. 95.  2000. Scaling of crack surfaces and implications for fracture mechanics. Phys. Rev. Lett. 85:1678–81 [Google Scholar]
  96. Måløy KJ, Hansen A, Hinrichsen EL, Roux S. 96.  1992. Experimental measurements of the roughness of brittle cracks. Phys. Rev. Lett. 68:213–15 [Google Scholar]
  97. Hansen A, Schmittbuhl J. 97.  2003. Origin of the universal roughness exponent of brittle fracture surfaces: stress-weighted percolation in the damage zone. Phys. Rev. Lett. 90:045504 [Google Scholar]
  98. Schmittbuhl J, Hansen A, Batrouni GG. 98.  2003. Roughness of interfacial crack fronts: stress-weighted percolation in the damage zone. Phys. Rev. Lett. 90:045505 [Google Scholar]
  99. Laurson L, Santucci S, Zapperi S. 99.  2010. Avalanches and clusters in planar crack front propagation. Phys. Rev. E 81:046116 [Google Scholar]
  100. Schmittbuhl J, Roux S, Vilotte JP, Måløy KJ. 100.  1995. Interfacial crack pinning: effect of nonlocal interactions. Phys. Rev. Lett. 74:1787–90 [Google Scholar]
  101. Rosso A, Krauth W. 101.  2002. Roughness at the depinning threshold for a long-range elastic string. Phys. Rev. E 65:025101 [Google Scholar]
  102. Mecholsky J, Passoja D, Feinberg-Ringel K. 102.  1989. Quantitative analysis of brittle fracture surfaces using fractal geometry. J. Am. Ceram. Soc. 72:60–65 [Google Scholar]
  103. Mecholsky J, Mackin T, Passoja D. 103.  1988. Self-similar crack propagation in brittle materials. Adv. Ceram. 22:127–34 [Google Scholar]
  104. Mecholsky JJ, Freiman SW. 104.  1991. Relationship between fractal geometry and fractography. J. Am. Ceram. Soc. 74:3136–38 [Google Scholar]
  105. Tsai Y, Mecholsky J. 105.  1991. Fractal fracture of single crystal silicon. J. Mater. Res. 6:1248–63 [Google Scholar]
  106. Schmittbuhl J, Måløy KJ. 106.  1997. Direct observation of a self-affine crack propagation. Phys. Rev. Lett. 78:3888–91 [Google Scholar]
  107. Schmittbuhl J, Schmitt F, Scholz C. 107.  1995. Scaling invariance of crack surfaces. J. Geophys. Res. Solid Earth 100:5953–73 [Google Scholar]
  108. Schmittbuhl J, Gentier S, Roux S. 108.  1993. Field measurements of the roughness of fault surfaces. Geophys. Res. Lett. 20:639–41 [Google Scholar]
  109. Santucci S, Måløy KJ, Delaplace A, Mathiesen J, Hansen A. 109.  et al. 2007. Statistics of fracture surfaces. Phys. Rev. E 75:016104 [Google Scholar]
  110. Chen YJ, Zapperi S, Sethna JP. 110.  2015. Crossover behavior in interface depinning. Phys. Rev. E 92:022146 [Google Scholar]
  111. Talreja R, Weibull W. 111.  1977. Probability of fatigue failure based on residual strength. Proceedings ICF4 Oxford, UK: Pergamon Press [Google Scholar]
  112. Jayatilaka AdS, Trustrum K. 112.  1977. Statistical approach to brittle fracture. J. Mater. Sci. 12:1426–30 [Google Scholar]
  113. Phoenix SL, Taylor HM. 113.  1973. The asymptotic strength distribution of a general fiber bundle. Adv. Appl. Probab. 5:200–16 [Google Scholar]
  114. Györgyi G, Moloney N, Ozogány K, Rácz Z, Droz M. 114.  2010. Renormalization-group theory for finite-size scaling in extreme statistics. Phys. Rev. E 81:041135 [Google Scholar]
  115. Györgyi G, Moloney N, Ozogány K, Rácz Z. 115.  2008. Finite-size scaling in extreme statistics. Phys. Rev. Lett. 100:210601 [Google Scholar]
  116. Salminen L, Tolvanen A, Alava MJ. 116.  2002. Acoustic emission from paper fracture. Phys. Rev. Lett. 89:185503 [Google Scholar]
  117. Koivisto J, Rosti J, Alava MJ. 117.  2007. Creep of a fracture line in paper peeling. Phys. Rev. Lett. 99:145504 [Google Scholar]
  118. Hemmer PC, Hansen A. 118.  1992. The distribution of simultaneous fiber failures in fiber bundles. J. Appl. Mech. 59:909–14 [Google Scholar]
  119. Shekhawat A, Zapperi S, Sethna JP. 119.  2013. From damage percolation to crack nucleation through finite-size criticality. Phys. Rev. Lett. 110:185505 [Google Scholar]
  120. Fisher DS. 120.  1998. Collective transport in random media: from superconductors to earthquakes. Phys. Rep. 301:113–50 [Google Scholar]
  121. Zaiser M, Moretti P. 121.  2005. Fluctuation phenomena in crystal plasticity: a continuum model. J. Stat. Mech. Theory Exp. 2005:P08004 [Google Scholar]
  122. Zaiser M. 122.  2006. Scale invariance in plastic flow of crystalline solids. Adv. Phys. 55:185–245 [Google Scholar]
  123. Talamali M, Petäjä V, Vandembroucq D, Roux S. 123.  2011. Avalanches, precursors, and finite-size fluctuations in a mesoscopic model of amorphous plasticity. Phys. Rev. E 84:016115 [Google Scholar]
  124. Durin G, Zapperi S. 124.  2006. The Barkhausen effect. The Science of Hysteresis, ed. G Bertotti, ID Mayergoyz, pp. 181–267 Oxford, UK: Academic Press [Google Scholar]
  125. Narayan O, Fisher DS. 125.  1993. Threshold critical dynamics of driven interfaces in random media. Phys. Rev. B 48:7030–42 [Google Scholar]
  126. Leschhorn H, Nattermann T, Stepanow S, Tang LH. 126.  1997. Driven interface depinning in a disordered medium. Ann. Phys. 509:1–34 [Google Scholar]
  127. Chauve P, Giamarchi T, Le Doussal P. 127.  2000. Creep and depinning in disordered media. Phys. Rev. B 62:6241–67 [Google Scholar]
  128. Chauve P, Le Doussal P, Wiese KJ. 128.  2001. Renormalization of pinned elastic systems: How does it work beyond one loop?. Phys. Rev. Lett. 86:1785–88 [Google Scholar]
  129. Le Doussal P, Wiese KJ, Chauve P. 129.  2002. Two-loop functional renormalization group theory of the depinning transition. Phys. Rev. B 66:174201 [Google Scholar]
  130. Kagan YY. 130.  2010. Earthquake size distribution: power-law with exponent β=1/2?. Tectonophysics 490:103–14 [Google Scholar]
  131. Ben-Zion Y. 131.  2008. Collective behavior of earthquakes and faults: continuum-discrete transitions, progressive evolutionary changes, and different dynamic regimes. Rev. Geophys. 46:RG4006 [Google Scholar]
  132. Baró J, Corral A, Illa X, Planes A, Salje EKH. 132.  et al. 2013. Statistical similarity between the compression of a porous material and earthquakes. Phys. Rev. Lett. 110:088702 [Google Scholar]
  133. Fisher DS, Dahmen KA, Ramanathan D, Ben-Zion Y. 133.  1997. Statistics of earthquakes in simple models of heterogeneous faults. Phys. Rev. Lett. 78:4885–88 [Google Scholar]
  134. Chen K, Bak P, Obukhov SP. 134.  1991. Self-organized criticality in a crack-propagation model of earthquakes. Phys. Rev. A 43:625–30 [Google Scholar]
  135. Carlson JM, Langer JS. 135.  1989. Properties of earthquakes generated by fault dynamics. Phys. Rev. Lett. 62:2632–35 [Google Scholar]
  136. Langer J, Carlson J, Myers CR, Shaw BE. 136.  1996. Slip complexity in dynamic models of earthquake faults. PNAS 93:3825–29 [Google Scholar]
  137. Dahmen K, Ertaş D, Ben-Zion Y. 137.  1998. Gutenberg-richter and characteristic earthquake behavior in simple mean-field models of heterogeneous faults. Phys. Rev. E 58:1494–501 [Google Scholar]
  138. Liu AJ, Nagel SR. 138.  2010. The jamming transition and the marginally jammed solid. Annu. Rev. Condens. Matter Phys. 1:347–69 [Google Scholar]
  139. Liu AJ, Nagel SR, van Saarloos W, Wyart M. 139.  2011. The jamming scenario—an introduction and outlook. Dynamical Heterogeneities in Glasses, Colloids, and Granular Media L Berthier, G Biroli, J-P Bouchard, L Cipelletti, W van Saarloos, pp. 1–72 New York/Oxford, UK: Oxford Univ. Press [Google Scholar]
  140. Ispánovity PD, Laurson L, Zaiser M, Groma I, Zapperi S, Alava MJ. 140.  2014. Avalanches in 2D dislocation systems: Plastic yielding is not depinning. Phys. Rev. Lett. 112:235501 [Google Scholar]
  141. Bi D, Yang X, Marchetti MC, Manning ML. 141.  2016. Motility-driven glass and jamming transitions in biological tissues. Phys. Rev. X 6:021011 [Google Scholar]
  142. Tsekenis G, Goldenfeld N, Dahmen KA. 142.  2011. Dislocations jam at any density. Phys. Rev. Lett. 106:105501 [Google Scholar]
  143. Miguel MC, Vespignani A, Zaiser M, Zapperi S. 143.  2002. Dislocation jamming and Andrade creep. Phys. Rev. Lett. 89:165501 [Google Scholar]
  144. Goodrich CP, Liu AJ, Sethna JP. 144.  2016. Scaling ansatz for the jamming transition. PNAS 113:9745–50 [Google Scholar]
  145. Hatano T. 145.  2008. Scaling properties of granular rheology near the jamming transition. J. Phys. Soc. Jpn. 77:123002 [Google Scholar]
  146. Tighe BP, Woldhuis E, Remmers JJC, van Saarloos W, van Hecke M. 146.  2010. Model for the scaling of stresses and fluctuations in flows near jamming. Phys. Rev. Lett. 105:088303 [Google Scholar]
  147. Dinkgreve M, Paredes J, Michels MAJ, Bonn D. 147.  2015. Universal rescaling of flow curves for yield-stress fluids close to jamming. Phys. Rev. E 92:012305 [Google Scholar]
  148. Nieh TG, Wadsworth J, Sherby OD. 148.  2005. Superplasticity in Metals and Ceramics Cambridge, UK: Cambridge Univ. Press
  149. Pázmándi F, Zaránd G, Zimányi GT. 149.  2000. Self-organized criticality in the hysteresis of the Sherrington–Kirkpatrick model. Physica B Condens. Matter 275:207–11 [Google Scholar]
  150. Lin J, Wyart M. 150.  2016. Mean-field description of plastic flow in amorphous solids. Phys. Rev. X 6:011005 [Google Scholar]
  151. Dahmen KA, Ben-Zion Y, Uhl JT. 151.  2009. Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Phys. Rev. Lett. 102:175501 [Google Scholar]
  152. Sun BA, Yu HB, Jiao W, Bai HY, Zhao DQ, Wang WH. 152.  2010. Plasticity of ductile metallic glasses: a self-organized critical state. Phys. Rev. Lett. 105:035501 [Google Scholar]
  153. Antonaglia J, Wright WJ, Gu X, Byer RR, Hufnagel TC. 153.  et al. 2014. Bulk metallic glasses deform via slip avalanches. Phys. Rev. Lett. 112:155501 [Google Scholar]
  154. Liu C, Ferrero EE, Puosi F, Barrat JL, Martens K. 154.  2016. Driving rate dependence of avalanche statistics and shapes at the yielding transition. Phys. Rev. Lett. 116:065501 [Google Scholar]
  155. Budrikis Z, Fernandez-Castellanos D, Sandfeld S, Zaiser M, Zapperi S. 155.  2015. Universality of avalanche exponents in plastic deformation of disordered solids. arXiv:1511.06229 [cond-mat.mtrl-sci]
  156. Salerno KM, Robbins MO. 156.  2013. Effect of inertia on sheared disordered solids: critical scaling of avalanches in two and three dimensions. Phys. Rev. E 88:062206–15 [Google Scholar]
  157. Bak P, Tang C, Wiesenfeld K. 157.  1988. Self-organized criticality. Phys. Rev. A 38:364–74 [Google Scholar]
  158. Rollett A, Humphreys F, Rohrer GS, Hatherly M. 158.  2004. Recrystallization and Related Annealing Phenomena Amsterdam: Elsevier
  159. Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S. 159.  2007. Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318:251–54 [Google Scholar]
  160. Zaiser M, Marmo B, Moretti P. 160.  2005. The yielding transition in crystal plasticity—discrete dislocations and continuum models. Proceedings of the International Conference on Statistical Mechanics of Plasticity and Related Instabilities Bangalore: Indian Inst. Sci. [Google Scholar]
  161. Tsekenis G, Uhl JT, Goldenfeld N, Dahmen KA. 160a.  2013. Determination of the universality class of crystal plasticity. Europhys. Lett. 101:336003 [Google Scholar]
  162. Lehtinen A, Costantini G, Alava MJ, Zapperi S, Laurson L. 161.  2016. Glassy features of crystal plasticity. Phys. Rev. B 94:064101 [Google Scholar]
  163. Papanikolaou S, Dimiduk DM, Choi W, Sethna JP, Uchic MD. 162.  et al. 2012. Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator. Nature 490:517–21 [Google Scholar]
  164. Jagla EA, Landes FP, Rosso A. 163.  2014. Viscoelastic effects in avalanche dynamics: a key to earthquake statistics. Phys. Rev. Lett. 112:174301 [Google Scholar]
  165. Pázmándi F, Zaránd G, Zimányi GT. 164.  1999. Self-organized criticality in the hysteresis of the Sherrington-Kirkpatrick model. Phys. Rev. Lett. 83:1034–37 [Google Scholar]
  166. Rutenberg AD, Vollmayr-Lee BP. 165.  1999. Anisotropic coarsening: grain shapes and nonuniversal persistence. Phys. Rev. Lett. 83:3772–75 [Google Scholar]
  167. Shore JD, Holzer M, Sethna JP. 166.  1992. Logarithmically slow domain growth in nonrandomly frustrated systems: Ising models with competing interactions. Phys. Rev. B 46:11376–404 [Google Scholar]
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