A Unifying Phase Diagram for the Dynamics of Sheared Solids and Granular Materials

Pure and Applied Geophysics

Volumn 168, Issue 12, 2011, Pages 2221-2237

  Ben Zion, Yehuda ^a   Dahmen, Karin A ^b   Uhl, Jonathan T ^c  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c NONE

Author keywords

brittle deformation; damaged rocks; granular mechanics; irreversible deformation; phase transitions; plastic deformation; solid mechanics

Indexed keywords

BRITTLE DEFORMATION; BRITTLE SOLIDS; DYNAMIC REGIMES; DYNAMIC STRENGTH; EARTHQUAKE FAULT; FAILURE EVENTS; FUTURE OBSERVATIONS; GRANULAR MECHANICS; IRREVERSIBLE DEFORMATION; MEAN FIELD; MODE-SWITCHING; OBSERVATIONAL DATA; POWER-LAW STATISTICS; QUASI-PERIODICITIES; RATE-CONTROLLING; SCALE-INVARIANT; SCALING PREDICTION; SIMULATION DATA; SOLID MECHANICS; SPATIAL RESPONSE; STRESS TRANSFER; SYSTEM SIZE; TUNING PARAMETER;

COMPUTER SIMULATION; DYNAMICS; FORECASTING; GRANULAR MATERIALS; PHASE DIAGRAMS; PHASE TRANSITIONS; PLASTIC DEFORMATION; SHEAR DEFORMATION;

STRENGTH OF MATERIALS;

BRITTLE DEFORMATION; DEFORMATION MECHANISM; EXPERIMENTAL STUDY; FAILURE MECHANISM; GRANULAR MEDIUM; PARAMETERIZATION; PLASTIC DEFORMATION; POWER LAW; ROCK MECHANICS; SHEAR STRENGTH;

EID: 80051781066     PISSN: 00334553     EISSN: 14209136     Source Type: Journal    
DOI: 10.1007/s00024-011-0273-7     Document Type: Article

References (63)

1. Aharonov, E., and D. Sparks (1999), Rigidity phase transition in granular packings, Phys. Rev E, 60, 6890-6896.
2. Aharonov, E., and D. Sparks (2002), "Shear profiles and localization in simulations of granular materials", Phys. Rev. E 65, 051302/1-12.
3. Aharonov, E., and D. Sparks (2004), Stick-slip motion in simulated granular layers, J. Geophys. Res, 109, B09306.
4. Alava, M. J., P. K. V. V. Nukala, and S. Zapperi (2006), Statistical models of fracture, Advances in Physics, 55, 349-476.
5. Amit, R., E. Zilberman, N. Porat, and Y. Enzel (2002), Paleoseismic evidence for time-dependency of seismic response on a fault system - the southern Arava Valley, Red Sea Rift, Israel, Geol. Soc. Am. Bull., 114, 192-206.
6. Ashby, M. F., and C. G. Sammis (1990), The damage mechanics of brittle solids in compression, Pure Appl. Geophys., 133 (3), 489-521.
7. Baldassari A., et al. (2006), Brownian forces in sheared granular matter, Phys. Rev. Lett. 96, 118002.
8. Baud, P., E. Klein, and T.-F. Wong (2004), Compaction localization in porous sandstones: spatial evolution of damage and acoustic emission activity J. Struct. Geol., 26, 603-624.
9. Ben-David, O., S. M. Rubinstein and J. Fineberg (2010), Slip-stick and the evolution of frictional strength, Nature, 463, 76-79.
10. Ben-Zion, Y., and J. R. Rice (1993), Earthquake failure sequences along a cellular fault zone in a three-dimensional elastic solid containing asperity and nonasperity regions, J. Geophys. Res., 98, 14109-14131.
11. Ben-Zion, Y. (1996), Stress, slip and earthquakes in models of complex single-fault systems incorporating brittle and creep deformations, J. Geophys. Res., 101, 5677-5706.
12. Ben-Zion, Y., K. Dahmen, V. Lyakhovsky, D. Ertas, and A. Agnon (1999), Self-Driven Mode Switching of Earthquake Activity on a Fault System, Earth Planet. Sci. Lett., 172/1-2, 11-21.
13. Ben-Zion, Y., M. Eneva, and Y. Liu (2003), Large Earthquake Cycles and Intermittent Criticality On Heterogeneous Faults Due To Evolving Stress and Seismicity, J. Geophys. Res., 108, No. B6, 2307. doi: 10. 1029/2002JB002121.
14. Ben-Zion, Y., and V. Lyakhovsky (2006), Analysis of Aftershocks in a Lithospheric Model with Seismogenic Zone Governed by Damage Rheology, Geophys. J. Int., 165, 197-210. doi: 10. 1111/j. 1365-246X. 2006. 02878. x.
15. Ben-Zion, Y. (2008), Collective behavior of earthquakes and faults: Continuum-discrete transitions, progressive evolutionary changes and different dynamic regimes, Rev. Geophys. 46, RG4006. doi: 10. 1029/2008RG000260.
16. Bruhn, R. L., W. T. Parry, W. A. Yonkee, and T. Thompson (1994), Fracturing and hydrothermal alteration in normal fault zones, Pure Appl. Geophys., 142, 609-645.
17. Bulatov, V. V., and A. S. Argon (1994), A stochastic model for continuum elasto-plastic behavior. I. Numerical approach and strain localization, Model. Simul. Mater. Sci. Eng. 2, 167.
18. Chen, K., P. Bak, and S. P. Obukhov (1991), "Self Organized Criticality in a crack-propagation model of earthquakes", Phys. Rev. A 43, 625-630.
19. Chester, F. M., J. P. Evans, and R. L. Biegel (1993), Internal structure and weakening mechanisms of the San Andreas fault, J. Geophys. Res., 98, 771-786.
20. Chinnery, M. (1963), The stress changes that accompany strike-slip faulting, Bull. Seismol. Soc. Amer., 53, 921-932.
21. Csikor, F. F., C. Motz, D. Weygand, M. Zaiser, and S. Zapperi (2007), 'Dislocation Avalanches, Strain Bursts, and the Problem of Plastic Forming at the Micrometer Scale', Science 318, 251-254.
22. Dahmen, K., D. Ertas, and Y. Ben-Zion (1998), Gutenberg Richter and Characteristic Earthquake behavior in Simple Mean-Field Models of Heterogeneous Faults, Phys. Rev. E, 58, 1494-1501.
23. Dahmen, K., and Y. Ben-Zion (2009), The physics of jerky motion in slowly driven magnetic and earthquake fault systems, Encyclopedia of Complexity and System Science, R. Meyers (Eds.), Vol. 5, 5021-5037, Springer.
24. Dahmen, K. A., Y. Ben-Zion, and J. T. Uhl (2009), A micromechanical model for deformation in disordered solids with universal predictions for stress-strain curves and related avalanches, Phys. Rev. Lett., 102, 175501. doi: 10. 1103/PhysRevLett. 102. 175501.
25. Dahmen, K. A., Y. Ben-Zion, and J. T. Uhl (2011), A simple analytic theory for the statistics of avalanches in sheared granular materials, Nature Physics, 7, 554-557. doi: 10. 1038/NPHYS1957.
26. Daniels, K. E., and N. W. Hayman (2008), "Force chains in seismogenic faults visualized with photoelastic granular shear experiments" Journal of Geophysical Research, 113 B11411 and references therein.
27. Dieterich, J. H., and B. D. Kilgore (1996), Imaging surface contacts; power law contact distributions and contact stresses in quarts, calcite, glass, and acrylic plastic. Tectonophysics, 256, 219-239.
28. Dimiduk, D. M., C. Woodward, R. LeSar, and M. D. Uchic (2006), "Scale-Free Intermittent Flow in Crystal Plastity", Science 312, 1188-1190.
29. Falk, M. L., and J. S. Langer (1998), Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, 57(6), 7192-7205.
30. Fisher, D. S., K. Dahmen, S. Ramanathan, and Y. Ben-Zion (1997), Statistics of Earthquakes in Simple Models of Heterogeneous Faults, Phys. Rev. Lett., 78, 4885-4888.
31. Fisher, D. S. (1998), Collective transport in random media: from superconductors to earthquakes, Phys. Reports, 301, 113-150.
32. Hartley, R. R. (2004), Evolving force networks in deforming granular materials, PhD thesis, Duke University.
33. Hayman, N. W., L. Ducloue, K. L. Foco, K. E. Daniels (2011), Granular controls on periodicity of stick-slip events: kinematics and force-chains in an experimental fault, Pure and Applied Physics, in press.
34. Hickman, S. H., and B. Evans (1992), Growth of grain contacts in halite by solution transfer; Implications for diagenesis, lithification, and strength recovery, in Fault Mechanics and Transport Properties of Rocks, edited by B. Evans and T.-F. Wong, pp. 253-280, Academic, San Diego, Calif.
35. Jaeger, M., S. R. Nagel, and R. P. Behringer (1996), Granular solids, liquids, and gases, Rev. Mod. Phys., 68, 1259-1273.
36. Johnson, P. A., and X. Jia (2005), Nonlinear dynamics, granular media and dynamic earthquake triggering, Nature, 473, 871-874.
37. Kachanov, L. M. (1986), Introduction to continuum damage mechanics, pp. 135, Martinus Nijhoff Publishers.
38. Kuntz, M. and J. P. Sethna (2000), Noise in disordered systems: the power spectrum and dynamic exponents in avalanche models, Phys. Rev. B 62, 11699-11708.
39. Laurson, L., and M. J. Alava (2006), 1/f noise and avalanche scaling in plastic deformation, Phys. Rev. E 74, 066106.
40. Liu, A. J., and S. R. Nagel (eds) (2001), Jamming and Rheology, Taylor and Francis, New York.
41. Lyakhovsky, V., Y. Ben-Zion, and A. Agnon (2001), Earthquake Cycle, Fault Zones, and Seismicity Patterns in a Rheologically Layered Lithosphere, J. Geophys. Res., 106, 4103-4120.
42. Lyakhovsky, V. and Y. Ben-Zion (2008), Scaling relations of earthquakes and aseismic deformation in a damage rheology model, Geophys. J. Int., 172, 651-662. doi: 10. 1111/j. 1365-246X. 2007. 03652. x.
43. Lyakhovsky, V. and Y. Ben-Zion (2009), Evolving geometrical and material properties of fault zones in a damage rheology model, Geochem. Geophys. Geosyst., 10, Q11011. doi: 10. 1029/2009GC002543.
44. Maloney, C. E. and M. O. Robbins (2009), Anisotropic Power Law Strain Correlations in Sheared Amorphous 2D Solids, Phys. Rev. Lett. 102, 225502.
45. Marco, S., M. Stein, A. Agnon, and H. Ron (1996), Long term earthquake clustering: a 50, 000 year paleoseismic record in the Dead sea graben, J. Geophys. Res., 101, 6179-6192.
46. Marone, C. (1998), Laboratory-derived friction laws and their application to seismic faulting, Annu. Rev. Earth Planet. Sci., 26, 643-649.
47. Mehta, A. P., K. A. Dahmen, and Y. Ben-Zion (2006), Universal mean moment rate profiles of earthquake ruptures, Phys. Rev. E., 73, 056104.
48. Papanikolaou, S., F. Bohn, R. L. Sommer, G. Durin, S. Zapperi, and J. P. Sethna (2009), Beyond scaling: the average avalanche shape, arXiv: 0911. 2291.
49. Peng, Z., and Y. Ben-Zion (2006), Temporal changes of shallow seismic velocity around the Karadere-Duzce branch of the north Anatolian fault and strong ground motion, Pure Appl. Geophys., 163, 567-600. doi: 10. 1007/s00024-005-0034-6.
50. Petri, A., A. Baldassarri, F. Dalton, G. Pontuale, L. Pietronero, S. Zapperi, (2008) Stochastic dynamics of a sheared granular medium, EPJ B 64, 531.
51. Rechenmacher, A., Abedi, S. and Chupin, O. (2010), Evolution of Force Chains in Shear Bands in Sand, Geotechnique, 60, 343-351.
52. Richeton, T., J. Weiss, and F. Louchet (2005), Breakdown of avalanche critical behavior in polycrystalline plasticity, Nature Materials 4, 465-469.
53. Sethna, J. P., K. A. Dahmen, and C. R. Myers (2001), "Crackling Noise", Nature, 410, 242-250.
54. Spaepen, F. (1977), A microscopic mechanism for steady state inhomogeneous flow in metallic glasses, Acta Metallurgica 25, 407-415.
55. Tsekenis, G. and K. A. Dahmen (2010) Depinning without a Jamming Point in Dislocation Systems, Phys. Rev. Lett., submitted.
56. Turcotte, D. L. (1997), Fractals and Chaos in Geology and Geophysics, Cambridge University Press.
57. Utsu, T., Y. Ogata, and R. S. Matsu'ura (1995), The centenary of the Omori Formula for a decay law of aftershock activity, J. Phys. Earth, 43, 1-33.
58. Weertman, J. (1996), Dislocation Based Fracture Mechanics, World Scientific.
59. Wong, T.-F., P. Baud and E. Klein (2001), Localized failure modes in a compactant porous rock. Geophys. Res. Lett. 28, 2521-2524.
60. Wu, C., Z. Peng, and Y. Ben-Zion (2009), Non-linearity and temporal changes of fault zone site response associated with strong ground motion, Geophys. J. Int., 176, 265-278. doi: 10. 1111/j. 1365-246X. 2008. 04005. x.
61. Yu, P., T. Shannon, B. Utter, R. P. Behringer (2009), Stick-Slip in a 2D Granular Medium", submitted.
62. Zaiser, M. (2006), Scale invariance in plastic flow of crystalline solids, Advances in Physics 55, 185-245.
63. Miguel M. C. and Zapperi, S. (2006), Fluctuations in plasticity at the microscale, Science 312, 1151-1152 and references therein.