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Sliding Without Slipping Under Coulomb Friction: Opening Waves and Inversion of Frictional Force

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Abstract

An elastic layer slides on a rigid flat governed by Coulomb’s friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick–slip pulses, which transform into opening waves propagating at intersonic speed in the direction of sliding or, for high Poisson’s ratios, at supersonic speed in the opposite direction. This sliding mode, characterized by marginal frictional dissipation, and similar to carpet fold propagation, may result in inversion of the frictional force direction; at longer time intervals, the system demonstrates stick–slip behavior. The mechanism is described in detail, and a parametric study is presented.

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Notes

  1. For a single case, the simulations were run also in commercial finite element software ABAQUS, which properly reproduced the results obtained with our software.

References

  1. Adams, G.G.: Steady sliding of two elastic half-spaces with friction reduction due to interface stick-slip. J. Appl. Mech. 65(2), 470–475 (1998)

    Article  Google Scholar 

  2. Adams, G.G.: Radiation of body waves induced by the sliding of an elastic half-space against a rigid surface. J. Appl. Mech. 67(1), 1–5 (2000)

    Article  Google Scholar 

  3. Adams, G.G.: Self-excited oscillations of two elastic half-spaces sliding with a constant coefficient of friction. J. Appl. Mech. 62(4), 867–872 (1995)

    Article  Google Scholar 

  4. Anderson, A., Knapp, R.: Hot spotting in automotive friction systems. Wear 135(2), 319–337 (1990)

    Article  Google Scholar 

  5. Andrews, D.: Rupture propagation with finite stress in antiplane strain. J. Geophys. Res. Solid Earth 81(20), 3575–3582 (1976)

    Article  Google Scholar 

  6. Andrews, D., Ben-Zion, Y.: Wrinkle-like slip pulse on a fault between different materials. J. Geophys. Res. Solid Earth 102(B1), 553–571 (1997)

    Article  Google Scholar 

  7. Barquins, M.: Sliding friction of rubber and Schallamach waves—a review. Mater. Sci. Eng. 73, 45–63 (1985)

    Article  Google Scholar 

  8. Baumberger, T., Caroli, C., Ronsin, O.: Self-healing slip pulses along a gel/glass interface. Phys. Rev. Lett. 88(7), 075509 (2002)

    Article  Google Scholar 

  9. Ben-David, O., Cohen, G., Fineberg, J.: The dynamics of the onset of frictional slip. Science 330(6001), 211 (2010)

    Article  Google Scholar 

  10. Ben-David, O., Fineberg, J.: Static friction coefficient is not a material constant. Phys. Rev. Lett. 106(25), 254301 (2011)

    Article  Google Scholar 

  11. Ben-Zion, Y., Huang, Y.: Dynamic rupture on an interface between a compliant fault zone layer and a stiffer surrounding solid. J. Geophys. Res. Solid Earth 107(B2), ESE-6 (2002)

  12. Besson, J., Foerch, R.: Large scale object-oriented finite element code design. Comput. Methods Appl. Mech. Eng. 142, 165–187 (1997)

    Article  Google Scholar 

  13. Bui, H.D., Oueslati, A.: On the stick-slip waves under unilateral contact and coulomb friction. Ann. Solid Struct. Mech. 1(3–4), 159–172 (2010)

    Article  Google Scholar 

  14. Carpinteri, A., Paggi, M.: Size-scale effects on the friction coefficient. Int. J. Solids Struct. 42(9), 2901–2910 (2005)

    Article  Google Scholar 

  15. Cochard, A., Rice, J.R.: Fault rupture between dissimilar materials: Ill-posedness, regularization, and slip-pulse response. J. Geophys. Res. Solid Earth 105(25), 891 (2000)

    Google Scholar 

  16. Coker, D., Lykotrafitis, G., Needleman, A., Rosakis, A.: Frictional sliding modes along an interface between identical elastic plates subject to shear impact loading. J. Mech. Phys. Solids 53(4), 884–922 (2005)

    Article  Google Scholar 

  17. Coker, D., Rosakis, A.J., Needleman, A.: Dynamic crack growth along a polymer composite–Homalite interface. J. Mech. Phys. Solids 51(3), 425–460 (2003)

    Article  Google Scholar 

  18. Comninou, M., Dundurs, J.: Elastic interface waves involving separation. J. Appl. Mech. 44(2), 222–226 (1977)

    Article  Google Scholar 

  19. Comninou, M., Dundurs, J.: Can two solids slide without slipping? Int. J. Solids Struct. 14(4), 251–260 (1978)

    Article  Google Scholar 

  20. Finite element software Z-set: www.zset-software.com

  21. Francavilla, A., Zienkiewicz, O.C.: A note on numerical computation of elastic contact problems. Int. J. Numer. Meth. Eng. 9, 913–924 (1975)

    Article  Google Scholar 

  22. Freund, L.: Discussion: ”Elastic interface waves involving separation“ (Comninou, M., and Dundurs, J., 1977, ASME J. Appl. Mech., 44, pp. 222–226). J. Appl. Mech. 45(1), 226–227 (1978)

  23. Gent, A.: Friction and wear of highly-elastic solids. Wear 29(1), 111–116 (1974)

    Article  Google Scholar 

  24. Gerde, E., Marder, M.: Friction and fracture. Nature 413(6853), 285–288 (2001)

    Article  Google Scholar 

  25. Heaton, T.H.: Evidence for and implications of self-healing pulses of slip in earthquake rupture. Phys. Earth Planet. Inter. 64(1), 1–20 (1990)

    Article  Google Scholar 

  26. Hilber, H.M., Hughes, T.J., Taylor, R.L.: Improved numerical dissipation for time integration algorithms in structural dynamics. Earthq. Eng. Struct. Dyn. 5(3), 283–292 (1977)

    Article  Google Scholar 

  27. Jean, M.: Frictional contact in collections of rigid or deformable bodies: numerical simulation of geomaterial motions. Mech. Geomater. Interfaces 42, 463–486 (1995)

    Article  Google Scholar 

  28. Kammer, D.S., Radiguet, M., Ampuero, J.P., Molinari, J.F.: Linear elastic fracture mechanics predicts the propagation distance of frictional slip. Tribol. Lett. 57(3), 1–10 (2015)

    Article  Google Scholar 

  29. Kammer, D.S., Yastrebov, V.A., Anciaux, G., Molinari, J.F.: The existence of a critical length scale in regularised friction. J. Mech. Phys. Solids 63, 40–50 (2014)

    Article  Google Scholar 

  30. Kammer, D.S., Yastrebov, V.A., Spijker, P., Molinari, J.F.: On the propagation of slip fronts at frictional interfaces. Tribol. Lett. 48(1), 27–32 (2012)

    Article  Google Scholar 

  31. Kawamura, H., Hatano, T., Kato, N., Biswas, S., Chakrabarti, B.K.: Statistical physics of fracture, friction, and earthquakes. Rev. Mod. Phys. 84(2), 839 (2012)

    Article  Google Scholar 

  32. Lakes, R., Lee, T., Bersie, A., Wang, Y.: Extreme damping in composite materials with negative-stiffness inclusions. Nature 410(6828), 565–567 (2001)

    Article  Google Scholar 

  33. Liu, C., Huang, Y., Rosakis, A.J.: Shear dominated transonic interfacial crack growth in a bimaterial i–ii. asymptotic fields and favorable velocity regimes. J. Mech. Phys. Solids 43(2), 189–206 (1995)

    Article  Google Scholar 

  34. Martins, J., Guimaraes, J., Faria, L.: Dynamic surface solutions in linear elasticity and viscoelasticity with frictional boundary conditions. J. Vib. Acoust. 117(4), 445–451 (1995)

    Article  Google Scholar 

  35. Moirot, F., Nguyen, Q.S., Oueslati, A.: An example of stick-slip and stick-slip-separation waves. Eur. J. Mech. A. Solids 22(1), 107–118 (2003)

    Article  Google Scholar 

  36. Müser, M.H., Wenning, L., Robbins, M.O.: Simple microscopic theory of Amontons’s laws for static friction. Phys. Rev. Lett. 86(7), 1295 (2001)

    Article  Google Scholar 

  37. Palmer, A.C., Rice, J.: The growth of slip surfaces in the progressive failure of over-consolidated clay. In: Proceedings of the Royal Society of London. Series A: Mathematical and physical sciences, vol. 332, pp. 527–548. The Royal Society (1973)

  38. Prakash, V., Clifton, R.J.: Time resolved dynamic friction measurements in pressure-shear. In: K. Ramesh (ed.) Experimental Techniques in the Dynamics of Deformable Solids, AMD-vol. 165, pp. 33–48. ASME, New York (1993)

  39. Ranjith, K., Rice, J.R.: Slip dynamics at an interface between dissimilar materials. J. Mech. Phys. Solids 49(2), 341–361 (2001)

    Article  Google Scholar 

  40. Renardy, M.: Ill-posedness at the boundary for elastic solids sliding under coulomb friction. J. Elast. 27(3), 281 (1992)

    Article  Google Scholar 

  41. Rice, J.R.: Constitutive relations for fault slip and earthquake instabilities. Pure Appl. Geophys. 121(3), 443–475 (1983)

    Article  Google Scholar 

  42. Radiguet, M., Kammer, D.S., Gillet, P., Molinari, J.F.: Survival of heterogeneous stress distributions created by precursory slip at frictional interfaces. Phys. Rev. Lett. 111(16), 164302 (2013)

    Article  Google Scholar 

  43. Schallamach, A.: How does rubber slide? Wear 17(4), 301–312 (1971)

    Article  Google Scholar 

  44. Scholz, C.H.: The Mechanics of Earthquakes and Faulting. Cambridge University Press, Cambridge (2002)

    Book  Google Scholar 

  45. Sørensen, M.R., Jacobsen, K.W., Stoltze, P.: Simulations of atomic-scale sliding friction. Phys. Rev. B 53(4), 2101–2113 (1996)

    Article  Google Scholar 

  46. Supplemental material: animation of formation of the stick-slip and stick-slip-opening pulse

  47. Svetlizky, I., Fineberg, J.: Classical shear cracks drive the onset of dry frictional motion. Nature 509(7499), 205–208 (2014)

    Article  Google Scholar 

  48. Urbakh, M., Klafter, J., Gourdon, D., Israelachvili, J.: The nonlinear nature of friction. Nature 430(6999), 525–528 (2004)

    Article  Google Scholar 

  49. Weertman, J.: Unstable slippage across a fault that separates elastic media of different elastic constants. J. Geophys. Res. Solid Earth 85(B3), 1455–1461 (1980)

    Article  Google Scholar 

  50. Wriggers, P.: Computational Contact Mechanics, 2nd edn. Springer, Berlin (2006)

    Book  Google Scholar 

  51. Xia, K., Rosakis, A.J., Kanamori, H.: Laboratory earthquakes: the sub-rayleigh-to-supershear rupture transition. Science 303(5665), 1859–61 (2004)

    Article  Google Scholar 

  52. Yastrebov, V.A.: Numerical Methods in Contact Mechanics. ISTE/Wiley, New York (2013)

    Book  Google Scholar 

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Acknowledgments

The author is grateful to David S. Kammer and Jean-Pierre Vilotte for valuable discussions.

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Correspondence to Vladislav A. Yastrebov.

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Yastrebov, V.A. Sliding Without Slipping Under Coulomb Friction: Opening Waves and Inversion of Frictional Force. Tribol Lett 62, 1 (2016). https://doi.org/10.1007/s11249-016-0650-6

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