Encyclopedia of Continuum Mechanics

Living Edition
| Editors: Holm Altenbach, Andreas Öchsner

Avalanches in Solids

Living reference work entry

Latest version View entry history

DOI: https://doi.org/10.1007/978-3-662-53605-6_73-2



Avalanches are domino-like processes where one event triggers another.

Bulk metallic glasses (BMGs) are noncrystalline metals, typically produced by rapid quenching and comprising three or more elements. The need for rapid quenching limits the thickness of metallic glasses in one dimension.

The complementary cumulative distribution C(S) of avalanche sizes S gives the probability of finding an avalanche with size greater than S.

A low-pass filter is an electronic circuit that passes signals with frequencies lower than a specified cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency.

Mean-field theory is an approximation to a model for which the physical interactions are replaced by infinite-range interactions in order to solve the model analytically.

A piezoelectric load cell is a sensor that generates a potential when a force is applied; the output is calibrated so that the sensor can be used...

This is a preview of subscription content, log in to check access.


  1. Antonaglia J, Wright WJ, Gu XJ, Byer RR, Hufnagel TC, LeBlanc M, Uhl JT, Dahmen KA (2014a) Bulk metallic glasses deform via slip-avalanches. Phys Rev Lett 112(15):155501/1–155501/4.  https://doi.org/10.1103/PhysRevLett.112.155501CrossRefGoogle Scholar
  2. Antonaglia J, Xie X, Schwarz G, Wraith M, Qiao JW, Zhang Y, Liaw PK, Uhl JT, Dahmen KA (2014b) Tuned critical avalanche scaling in bulk metallic glasses. Sci Rep 4:4382/1–4382/5.  https://doi.org/10.1038/srep04382CrossRefGoogle Scholar
  3. Baldassari A, Dalton F, Petri A, Zapperi S, Pontuale G, Pietronero L (2006) Brownian forces in sheared granular matter. Phys Rev Lett 96(11):118002/1–118002/4.  https://doi.org/10.1103/PhysRevLett.96.118002CrossRefGoogle Scholar
  4. Csikor FF, Motz C, Weygand D, Zaiser M, Zapperi S (2007) Dislocation avalanches, strain bursts, and the problem of plastic forming at the micrometer scale. Science 318(5848):251–254.  https://doi.org/10.1126/science.1143719CrossRefGoogle Scholar
  5. Daerr A, Douady S (1999) Two types of avalanche behaviour in granular media. Nature 399:241–243.  https://doi.org/10.1038/20392CrossRefGoogle Scholar
  6. Dahmen KA (2017) Mean field theory of slip statistics. In: Salje EKH, Saxena A, Planes A (eds) Avalanches in functional materials and geophysics. Understanding complex systems. Springer International Publishing AG, Cham, pp 19–30.  https://doi.org/10.1007/978-3-319-45612-6_2CrossRefGoogle Scholar
  7. Dahmen KA, Ben-Zion Y, Uhl JT (2009) Micromechanical model for deformation in solids with universal predictions for stress-strain curves and slip avalanches. Phys Rev Lett 102(17):175501/1–175501/4.  https://doi.org/10.1103/PhysRevLett.102.175501CrossRefGoogle Scholar
  8. Dahmen KA, Ben-Zion Y, Uhl JT (2011) A simple analytic theory for the statistics of avalanches in sheared granular materials. Nature Phys 7:554–557.  https://doi.org/10.1038/nphys1957CrossRefGoogle Scholar
  9. Dalla Torre FH, Klaumünzer D, Maaß R, Löffler JF (2010) Stick–slip behavior of serrated flow during inhomogeneous deformation of bulk metallic glasses. Acta Mater 58(10):3742–3750.  https://doi.org/10.1016/j.actamat.2010.03.011CrossRefGoogle Scholar
  10. Denisov DV, Lörìncz KA, Uhl JT, Dahmen KA, Schall P (2016) Universality of slip avalanches in flowing granular matter. Nat Commun 7:10641/1–10641/6.  https://doi.org/10.1038/ncomms10641CrossRefGoogle Scholar
  11. Denisov DV, Lörìncz KA, Wright WJ, Hufnagel TC, Nawano A, Gu XJ, Uhl JT, Dahmen KA, Schall P (2017) Universal slip dynamics in metallic glasses and granular matter: linking frictional weakening with inertial effects. Sci Rep 7:43376/1–43376/8.  https://doi.org/10.1038/srep43376CrossRefGoogle Scholar
  12. Fisher DS, Dahmen KA, Ramanathan S, Ben-Zion Y (1997) Statistics of earthquakes in simple models of heterogeneous faults. Phys Rev Lett 78(25):4885–4888.  https://doi.org/10.1103/PhysRevLett.78.4885CrossRefGoogle Scholar
  13. Friedman N, Jennings AT, Tsekenis G, Kim J-Y, Tao ML, Uhl JT, Greer JR, Dahmen KA (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(9):095507/1–095507/5.  https://doi.org/10.1103/PhysRevLett.109.095507CrossRefGoogle Scholar
  14. Han Z, Wu WF, Li Y, Wei YJ, Gao HJ (2009) An instability index of shear band for plasticity in metallic glasses. Acta Mater 57(5):1367–1372.  https://doi.org/10.1016/j.actamat.2008.11.018CrossRefGoogle Scholar
  15. Hartley R (2005) PhD thesis, Physics, Duke UniversityGoogle Scholar
  16. Hayman NW, Ducloué L, Foco KL, Daniels KE (2011) Granular controls on periodicity of stick-slip events: kinematics and force-chains in an experimental fault. Pure Appl Geophys 168:2239–2257.  https://doi.org/10.1007/s00024-011-0269-3CrossRefGoogle Scholar
  17. Kale S, Ostoja-Starzewski M (2014) Elastic-plastic-brittle transitions and avalanches in disordered media. Phys Rev Lett 112(4):045503/1–045503/5.  https://doi.org/10.1103/PhysRevLett.112.045503CrossRefGoogle Scholar
  18. Kavli Institute for Theoretical Physics (2014) A program on avalanches attempted to answer some of these questions. The talks and discussions of that workshop are posted here: http://www.kitp.ucsb.edu/activities/dbdetails?acro=nonequil14
  19. LeBlanc M, Angheluta L, Dahmen KA, Goldenfeld N (2012) Distribution of maximum velocities in avalanches near the depinning transition. Phys Rev Lett 109(10):105702.  https://doi.org/10.1103/PhysRevLett.109.105702CrossRefGoogle Scholar
  20. LeBlanc M, Angheluta L, Dahmen KA, Goldenfeld N (2013) Universal fluctuations and extreme statistics of avalanches near the depinning transition. Phys Rev E 87(2):022126.  https://doi.org/10.1103/PhysRevE.87.022126CrossRefGoogle Scholar
  21. LeBlanc M, Nawano A, Wright WJ, Gu XJ, Uhl JT, Dahmen KA (2016) Avalanche statistics from data with low time resolution. Phys Rev E 94(5):051235.  https://doi.org/10.1103/PhysRevE.94.052135CrossRefGoogle Scholar
  22. Lin J, Lerner E, Rosso A, Wyart M (2014) Scaling description of the yielding transition in soft amorphous solids at zero temperature. PNAS 111(40):14382–14387.  https://doi.org/10.1073/pnas.1406391111CrossRefGoogle Scholar
  23. Maaß R, Wraith M, Uhl JT, Greer JR, Dahmen KA (2015) Slip statistics of dislocation avalanches under different loading modes. Phys Rev E 91(4):042403/1–042403/8.  https://doi.org/10.1103/PhysRevE.91.042403CrossRefGoogle Scholar
  24. Majmudar TS, Behringer RP (2005) Contact force measurements and stress-induced anisotropy in granular materials. Nature 435:1079–1082.  https://doi.org/10.1038/nature03805CrossRefGoogle Scholar
  25. McFaul LW, Wright WJ, Gu XJ, Uhl JT, Dahmen KA (2018) to be publishedGoogle Scholar
  26. Nyquist H (2002) Certain topics in telegraph transmission theory (reprinted from 1928 trans AIEE February:617–644). Proc IEEE 90(2):280–305.  https://doi.org/10.1109/5.989875CrossRefGoogle Scholar
  27. Palassini M, Goethe M (2012) Elementary excitations and avalanches in the Coulomb glass. J Phys Conf Ser 376:012009/1–012009/6.  https://doi.org/10.1088/1742-6596/376/1/012009CrossRefGoogle Scholar
  28. Petri A, Baldassarri A, Dalton F, Pontuale G, Pietronero L, Zapperi S (2008) Stochastic dynamics of a sheared granular medium. Eur Phys J B 64(3–4):531–535.  https://doi.org/10.1140/epjb/e2008-00177-xCrossRefGoogle Scholar
  29. Ramanathan S, Fisher DS (1998) Onset of propagation of planar cracks in heterogeneous media. Phys Rev B 58(10):6026–6046.  https://doi.org/10.1103/PhysRevB.58.6026CrossRefGoogle Scholar
  30. Salerno KM, Maloney CE, Robbins MO (2012) Avalanches in strained amorphous solids: does inertia destroy critical behavior? Phys Rev Lett 109(10):105703/1–105703/5.  https://doi.org/10.1103/PhysRevLett.109.105703CrossRefGoogle Scholar
  31. Salje EKH, Dahmen KA (2014) Crackling noise in disordered materials. Annu Rev Condens Matter Phys 5:233–254.  https://doi.org/10.1146/annurev-conmatphys-031113-133838CrossRefGoogle Scholar
  32. Schwarz JM, Fisher DS (2001) Depinning with dynamic stress overshoots: mean field theory. Phys Rev Lett 87(9):096107/1–096107/4.  https://doi.org/10.1103/PhysRevLett.87.096107CrossRefGoogle Scholar
  33. Schwarz JM, Fisher DS (2003) Depinning with dynamical stress overshoots: a hybrid of critical and pseudohysteretic behavior. Phys Rev E 67(2):021603.  https://doi.org/10.1103/PhysRevE.67.021603CrossRefGoogle Scholar
  34. Sen S, Mousseau N, Overney G (1994) Onset of avalanches in granular media. Phys Rev E 49(5):4712–4715.  https://doi.org/10.1103/PhysRevE.49.4712CrossRefGoogle Scholar
  35. Sethna JP, Bierbaum MK, Dahmen KA, Goodrich CP, Greer JR, Hayden LX, Kent-Dobias JP, Lee ED, Liarte DB, Ni X, Quinn KN, Raju A, Rocklin DZ, Shekhawat A, Zapperi S (2017) Deformation of crystals: connections with statistical physics. Annu Rev Mater Res 47:217–246.  https://doi.org/10.1146/annurev-matsci-070115-032036CrossRefGoogle Scholar
  36. Shannon C (1998) Communication in the presence of noise (reprinted from 1949 proc IRE 37:10–21). Proc IEEE 86(2):447–457.  https://doi.org/10.1109/JPROC.1998.659497CrossRefGoogle Scholar
  37. Song SX, Wang X-L, Nieh TG (2010) Capturing shear band propagation in a Zr-based metallic glass using a high-speed camera. Scr Mater 62:847–850.  https://doi.org/10.1016/j.scriptamat.2010.02.017CrossRefGoogle Scholar
  38. Sun BA, Yu HB, Jiao W, Bai HY, Zhao DQ, Wang WH (2010) Plasticity of ductile metallic glasses: a self-organized critical state. Phys Rev Lett 105(3):035501/1–035501/4.  https://doi.org/10.1103/PhysRevLett.105.035501CrossRefGoogle Scholar
  39. Thomas H, Morfill GE, Demmel V, Goree J, Feuerbacher B, Möhlmann D (1994) Plasma crystal: coulomb crystallization in a dusty plasma. Phys Rev Lett 73(5):652–655.  https://doi.org/10.1103/PhysRevLett.73.652CrossRefGoogle Scholar
  40. Tsekenis G, Uhl JT, Goldenfeld N, Dahmen KA (2013) Determination of the universality class of crystal plasticity. Europhys Lett 101:360003/1–360003/6 and references therein.  https://doi.org/10.1209/0295-5075/101/36003CrossRefGoogle Scholar
  41. Uhl JT, Pathak S, Schorlemmer D, Liu X, Swindeman R, Brinkman BAW, LeBlanc M, Tsekenis G, Friedman N, Behringer R, Denisov D, Schall P, Gu XJ, Wright WJ, Hufnagel T, Jennings A, Greer JR, Liaw PK, Becker T, Dresen G, Dahmen KA (2015) Universal quake statistics: from compressed nanocrystals to earthquakes. Sci Rep 5:16493.  https://doi.org/10.1038/srep16493CrossRefGoogle Scholar
  42. White RA, Dahmen KA (2003) Driving rate effects on crackling noise. Phys Rev Lett 91(8):085702/1–085702/4.  https://doi.org/10.1103/PhysRevLett.91.085702CrossRefGoogle Scholar
  43. Wright WJ, Schwarz RB, Nix WD (2001) Localized heating during serrated plastic flow in bulk metallic glasses. Mater Sci Eng A 319–321:229–232.  https://doi.org/10.1016/s0921-5093(01)01066-8CrossRefGoogle Scholar
  44. Wright WJ, Samale MW, Hufnagel TC, LeBlanc MM, Florando JN (2009) Studies of shear band velocity using spatially and temporally resolved measurements of strain during quasistatic compression of a bulk metallic glass. Acta Mater 57(16):4639–4648.  https://doi.org/10.1016/j.actamat.2009.06.013CrossRefGoogle Scholar
  45. Wright WJ, Byer RR, Gu XJ (2013) High–speed imaging of a bulk metallic glass during uniaxial compression. Appl Phys Lett 102:241920.  https://doi.org/10.1063/1.4811744CrossRefGoogle Scholar
  46. Wright WJ, Liu Y, Gu XJ, Van Ness KD, Robare SL, Liu X, Antonaglia J, LeBlanc M, Uhl JT, Hufnagel TC, Dahmen KA (2016) Experimental evidence for both progressive and simultaneous shear during quasistatic compression of a bulk metallic glass. J Appl Phys 119:084908.  https://doi.org/10.1063/1.4942004CrossRefGoogle Scholar
  47. Zaiser M (2006) Scale invariance in plastic flow of crystalline solids. Adv Phys 55:185–245 and references therein.  https://doi.org/10.1080/00018730600583514CrossRefGoogle Scholar
  48. Zapperi S, Castellano C, Colaiori F, Durin G (2005) Signature of effective mass in crackling-noise asymmetry. Nature Phys 1:46–49.  https://doi.org/10.1038/nphys101CrossRefGoogle Scholar
  49. Zhang D, Dahmen KA, Ostoja-Starzewski M (2017) Scaling of slip avalanches in sheared amorphous materials based on large-scale atomistic simulations. Phys Rev E 95(3):032902/1–032902/12 and references therein.  https://doi.org/10.1103/PhysRevE.95.032902

Authors and Affiliations

  1. 1.Department of Physics and Institute for Condensed Matter TheoryUniversity of Illinois at Urbana ChampaignUrbanaUSA
  2. 2.Kavli Institute for Theoretical Physics, Kohn HallUniversity of California at Santa BarbaraSanta BarbaraUSA
  3. 3.Department of Mechanical Engineering, One Dent DriveBucknell UniversityLewisburgUSA
  4. 4.Department of Chemical Engineering, One Dent DriveBucknell UniversityLewisburgUSA

Section editors and affiliations

  • Martin Ostoja-Starzewski
    • 1
  1. 1.Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman InstituteUniversity of Illinois at Urbana–ChampaignUrbanaUSA