Pure and Applied Geophysics

, Volume 168, Issue 12, pp 2259–2275 | Cite as

Stick–Slip and the Transition to Steady Sliding in a 2D Granular Medium and a Fixed Particle Lattice

  • J. Krim
  • Peidong Yu
  • R. P. Behringer


We report an experimental study of the stick–slip to steady sliding behavior of a solid object pulled, via a spring, across 2D granular substrates of photoelastic disks that are either fixed in a solid lattice (granular solid) or unconstrained, forming a granular bed. We observe a progression of friction regimes with increasing sliding speed, including single-slip, double-slip, and mixed stick–slip regimes, steady sliding, and inertial oscillations. For the case of the granular bed, we report a detailed analysis of frictional behavior for the low speed stick–slip regime, including spring and elastic energy dependencies during the stick and slip portions of the motion. For the case of the granular solid, we explore friction in the presence and absence of externally applied vibrations, and compare it with sliding on a granular bed, which is intrinsically disordered. We observe that external vibration reduces transition values for both the single-slip to double-slip transition and the stick–slip to steady sliding transition. Moreover, we observe that the effect of packing disorder on granular friction seems similar to the effect of vibration-induced disorder, a result that, to our knowledge, has not been reported previously in the experimental literature.


Granular Material Slip Length Slip Event Force Chain Granular System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was supported by the US Army Research Office (grant W911NF-07-1-0131-00), by LANL Subcontract Number: 64898-001−08 (with P. Johnson and C. Marone), and by NSF-DMR0906908 and NSF-DMR0805204. We appreciate insightful discussions with M.O. Robbins.


  1. Aharanov, E. and Sparks, D. (2003) Stick–slip in granular material, J. Geophys. Res. 109, art #B09306Google Scholar
  2. Barel, I. and Urbakh, M. (2010), Multibond dynamics of Nanoscale friction: the role of temperature Phys. Rev. Lett. 104, art # 066104Google Scholar
  3. Baumberger, T., Berthoud, P. and Coroli, C. (1999), Physical analysis of the state- and rate-dependent friction law. II. Dynamic friction Phys. Rev. B 60, 3928-3939Google Scholar
  4. Behringer, R.P., Chakraborty, D. BI, B., Henkes, S. and Hartley, R. (2008), Title: Why Do Granular Materials Stiffen with Shear Rate? Test of Novel Stress-Based Statistics, Phys. Rev. Lett. 101, art #268301Google Scholar
  5. Ben-zion, Y (2001), Dynamic ruptures in recent models of earthquake faults, J. Mechanics and Physics of Solids 49, 2209-2244Google Scholar
  6. Ben-zion, Y. (2008) Collective Behavior of Earthquakes and Faults: Continuum-Discrete Transisitions, Porgressive Evolutionary Changes, and Different Dynamic Regimes Reviews of Geophysics 46, RG406, 1-70Google Scholar
  7. Borovsky, B., Krim, J., Syed Asif, S.A. and Wahl, K. (2001) Measuring Nanomechanical Properties of a Dynamic Contact Using an Indenter Probe and Quartz Crystal Microbalance, J. Appl. Phys. 90 6391-6396Google Scholar
  8. Bowden, F. P. and Tabor, D. (1954) , The Friction and Lubrication of Solids, Oxford University PressGoogle Scholar
  9. Braiman, Y., Hentschel, H.G.E., Family, F., Mak, C., and Krim, J. (1999), Tuning Friction with Noise and Disorder Phys. Rev. E 59(5), R4737-R4740.Google Scholar
  10. Braun, O.M., Peyrard, M., Bortolani, V., Franchini, A. and Vanossi (2005),Transition from smooth sliding to stick–slip motion in a single frictional contact Phys. Rev. E 72, art # 056116Google Scholar
  11. Burridge, R. and Knopoff, L. (1967), Model and Theoretical Seismicity Bull. Seismol. Soc. Am. 57, 3411Google Scholar
  12. Capozza, R., Vanossi, A., Vezzani, A., and Zapperi, S. (2009) Suppression of Friction by Mechanical Vibrations, Phys. Rev. Lett. 103, art # 085502Google Scholar
  13. Carlson, J. M., Langer, J. S. and Shaw, B. E. (1994) Dynamics of Earthquake faults, Rev. Mod. Phys. 66, 657−670Google Scholar
  14. Coulomb, C.A. (1773) Memoires deMathematique & de Physique, presentes a l’Academie Royale des Sciences par divers Savans et lus dan ses Assemblees, 7, 343-382Google Scholar
  15. Daniels, K.E. and Behringer, R.P. (2005), Hysteresis and competition between disorder and crystallization in sheared and vibrated granular flow., Phys. Rev. Lett. 94, art# 168001Google Scholar
  16. Daniels, K. E. and Hayman, N.W. (2008), Force chains in seismogenic faults visualized with photoelastic granular shear experiments Journal of Geophysical Research 113, art # B11411Google Scholar
  17. Dawson, B.D., Lee, S.M. and Krim, J. (2009), Tribo-Induced Melting Transition at a Sliding Asperity Contact, Phys. Rev. Lett. 103, art # 205502Google Scholar
  18. De Paola, N., Hirose, T., Mitchell, T., Di Toro, G., Viti, C. and Shimamoto, T. (2011) Fault lubrication and earthquake propagation in thermally unstable Rocks, Geology 39, 35-38Google Scholar
  19. Dieterich, J. H. (1972), Time-Dependent Friction in Rocks, J. Geophysical Research 77, 3690Google Scholar
  20. Edwards, S.F. and Oakeshott, R.B.S. (1989), Theory of Powders, Physica A 157, 1080-1090Google Scholar
  21. Elmer, F.-J. (1997), Nonlinear dynamics of dry friction, J. Phys. A. Math Gen. 30, 6057-6063Google Scholar
  22. Eyring, H., (1936), Viscosity, plasticity, and diffusion as examples of absolute reaction rates, J. Chem. Phys. 4, 283-291Google Scholar
  23. Fajardo, O.Y. and Mazo, J. J (2010), Title: Effects of surface disorder and temperature on atomic friction, Phys. Rev. B 82, art #035435Google Scholar
  24. Filippov, A.E., Klaftner, J., and Urbakh, M. (2004), Friction through dynamical formation and rupture of molecular bonds, Phys. Rev. Lett. 92, art #135503Google Scholar
  25. Geng, J., Behringer, R. P., Reydellet, G., and Clement, E. (2003), Green’s function measurements of force transmission in 2D granular materials, Physica D 182, 274303Google Scholar
  26. Goldhirsch, I., and Zanetti, G. (1993), Clustering Instabilty in Dissipative Gases, Phys. Rev. Lett. 70, 1619-1622Google Scholar
  27. Hartley, R. R. and Behringer, R. P. (2003), Logarithmic rate dependence of force networks in sheared granular materials, Nature 421, 928-930Google Scholar
  28. Henkes, S., O′hern, C.S. and Chakraborty, B. (2007), Entropy and temperature of a static granular assembly: An ab initio approach. Phys. Rev. Lett. 99, art# 038002Google Scholar
  29. Heslot, F., Baumberger, T., Perrin, B., Caroli, B. and Caroli, C.(1994) Creep, Stick–slip, and Dry-Friction dynamics- Experiments and a Heuristic Model,Phys. Rev. E 49, 4973-4988Google Scholar
  30. Howell, D.W., Behringer, R.P., and Veje, C.T. (1999), Fluctuations in granular media, Chaos 9, 559-572Google Scholar
  31. Jansen, L., Holscher, H., Fuchs, H. and Schirmeisen, A. (2010) Temperature Dependence of Atomic-Scale Stick–slip Friction, Phys. Rev. Lett. 104, art # 256101Google Scholar
  32. Jinesh, B., Yu, S., Krylov, H., Valk, Dienwiebel, M. and Frenken, J.W.M. (2008), Thermolubricity in atomic-scale friction, Phys. Rev. B 78 art # 155440Google Scholar
  33. Johnson, P.A. and Jia X. (2005), Nonlinear dynamics, granular media and dynamic earthquake triggering, Nature 437, 871-874Google Scholar
  34. Johnson, P., Savage, H., Knuth, M., Gomberg, J., and Marone, C. (2008), Effects of acoustic waves on stick–slip in granular media and implications for earthquakes, Nature 451, 47-60Google Scholar
  35. Krim, J. (1996) The Atomic-scale Origins of Friction, Langmuir, 12, 4564-4566Google Scholar
  36. Krim, J. (2002), Friction at Macroscopic and Microscopic Length Scales, Amer. J. Phys. 70, 890-897Google Scholar
  37. Krim, J and Berhinger, R.P. (2009), Friction, force chains, and falling fruit, Physics Today 62, 66-67Google Scholar
  38. Losert, W., Geminard, J.-C., Nasuno, S. and Gollub, J. P., (2000), Mechanisms for slow strengthening in granular materials, Phys.Rev. E 61 4060-4068Google Scholar
  39. Luan, B. and Robbins, M.O. (2004), Effect of inertia and elasticity on stick–slip motion, Phys. Rev. Lett. 93, art # 036105Google Scholar
  40. Mak, C. and Krim, J. (1997), Quartz crystal microbalance studies of disorder-induced lubrication, Faraday Discussions 107, 389-397Google Scholar
  41. Makse, H. A. and Kurchan J. (2002) Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment Nature 415, 614-617Google Scholar
  42. Majmudar, T. S. and Behringer,R. P. (2005), Title: Contact force measurements and stress-induced anisotropy in granular materials, Nature 435, 1079-1082Google Scholar
  43. Majmudar, T. S., Sperl, M., Luding, S. and Behringer, R. P. (2007), Jamming transition in granular systems, Phys.Rev. Lett. 98, art #058001Google Scholar
  44. Marone, C., Raleigh, C. B. and Scholz, C. H. (1990), Frictional behavior and constitutive modeling of simulated fault gouge, J. Geophysical Research 95, 7007-7025Google Scholar
  45. McFadden, C.F. and Gellman, A.J., (1997) Metallic friction: the influence of atomic adsorbates at submonolayer coverages, Surf. Sci. 391, 287-299Google Scholar
  46. Melosh, H.J., (1979) Acoustic Fluidization-New Geologicprocess, J. Geophysical Research 84, 7513-7520Google Scholar
  47. Muser, M. H., Urbakh, M. and Robbins, M. O. (2003), Statistical mechanics of static and low-velocity kinetic friction, Advances in Chemical Physics 126, 187-272Google Scholar
  48. Nakamura, J., Wakunami, S. and Natori, A. (2005) Double-slip mechanism in atomic-scale friction: Tomlinson model at finite temperatures, Phys. Rev. B 72, art # 235415Google Scholar
  49. Nasuno, S., Kudrolli, A. and Gollub, J. P., (1997a), Friction in granular layers: Hysteresis and precursors, Phys. Rev. Lett. 79 949-952Google Scholar
  50. Nasuno, S., Kudrolli, A. and Gollub, J. P., (1997) Sensitive force measurements in a sheared granular flow with simultaneous imaging, Powders & Grains 97,329-332, R. P. Behringer and J. T. Jenkins, eds., Balkema, Rotterdam, 1997Google Scholar
  51. Nowak, E.R., Knight, J.B., Povinelli, M.L., Jaeger, H.M. and Nagel, S.R. (1997), Reversibility and irreversibility in the packing of vibrated granular material Powder Technol. 94, 79-83Google Scholar
  52. Panella, V., Chiarello, R. and Krim, J. (1996), Adequacy of the Lifshitz theory for certain thin adsorbed films, Phys. Rev. Lett. 76, 3606-3609Google Scholar
  53. Robbins. M.O., and Krim, J. (1998), Energy Dissipation in interfacial friction, MRS Bulletin 23, 23-25Google Scholar
  54. Ruina, A. (1983), Slip instability and state variable friction laws, Jour. Geophysical Research 88, 359-370Google Scholar
  55. Siavoshi, S., Orpe,A. V. and Kudrolli, A. (2006), Friction of a slider on a granular layer: Nonmonotonic thickness dependence and effect of boundary conditions, Phys. Rev. E 73, art #010301(R)Google Scholar
  56. Socoliuc, A., Gnecco, E., Maier, S., Pfeifer, O., Baratoff, A., Bennewitz,R. and Meyer, E. (2006), Atomic-scale control of friction by actuation of nanometer-sized contacts Science 313, 207-210Google Scholar
  57. Tsai, J.-C., Voth, G. A., and Gollub, J.P. (2003), Internal Granular Dynamics, Shear-Induced Crystallization, and Compaction Steps, Phys. Rev. Lett 91, 064301Google Scholar
  58. Tshiprut, Z., Zelner, S. and Urbakh, M. (2009) Temperature-Induced Enhancement of Nanoscale Friction, Phys. Rev. Lett 102, art # 136102Google Scholar
  59. Yu, Peidong and Behringer, R.P. (2005), Granular Friction: A Slider Experiment Chaos 15 041102Google Scholar
  60. Yu, P., Shannon, T., Utter, B. and Begringer, R.P., (2011) Stick–slip in a 2D granular Medium, Preprint.Google Scholar
  61. Zhang, J., Majmudar, T. S., Tordesillas, A. and Behringer, R. P. (2010) Statistical properties of a 2D granular material subjected to cyclic shear, Granular Matter. 12, 159-172Google Scholar

Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of PhysicsDuke UniversityDurhamUSA
  2. 2.NC State UniversityRaleighUSA
  3. 3.German Aerospace CenterInstitute of Materials Physics in SpaceCologneGermany

Personalised recommendations