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Shock wave due to the short-period impact in one-dimensional plasticity bead chain

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Abstract.

The waves in a one-dimensional (1-D) bead chain produced by a constant velocity impact in a short period are studied numerically in the present paper. It seems that in some cases, the waves look like a shock wave, while in other cases they may be composed of several solitary waves or some oscillations. These characteristics depend on both the bead parameters and the impact parameters, such as the plasticity of the bead material, the piston velocity and the impact duration. It is found that the shock structure appears if the duration of the impact is longer, while it will evolve into several solitary waves if the duration of the impact is small enough. This indicates that the bead velocity attenuates with power function. The strength of the attenuation depends on the plasticity, the piston velocity and the bead radius.

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References

  1. Sylvain Courrech du Pont, Philippe Gondret, Bernard Perrin, Marc Rabaud, Phys. Rev. Lett. 90, 044301 (2003)

    Article  ADS  Google Scholar 

  2. Leopoldo R. Gomez, Ari M. Turner, Vincenzo Vitelli, Phys. Rev. E 86, 041302 (2012)

    Article  ADS  Google Scholar 

  3. Shu Jia, Wenjie Wan, Jason W. Fleischer, Phys. Rev. Lett. 99, 223901 (2007)

    Article  ADS  Google Scholar 

  4. Pedro Franco Navarro, David J. Benson, Vitali F. Nesterenko, Phys. Rev. E 94, 033002 (2016)

    Article  ADS  Google Scholar 

  5. S. Catheline, J.-L. Gennisson, M. Tanter, M. Fink, Phys. Rev. Lett. 91, 164301 (2003)

    Article  ADS  Google Scholar 

  6. Ue-Li Pen, Neil Turok, Phys. Rev. Lett. 117, 131301 (2016)

    Article  ADS  Google Scholar 

  7. Siet van den Wildenberg, Rogier van Loo, Martin van Hecke, Phys. Rev. Lett. 111, 218003 (2013)

    Article  ADS  Google Scholar 

  8. V. Karpman, Nonlinear Waves in Dispersive Media (Pergamon Press, New York, 1975)

  9. W.G. Ellenbroek, E. Somfai, M. van Hecke, W. van Saarloos, Phys. Rev. Lett. 97, 258001 (2006)

    Article  ADS  Google Scholar 

  10. A. Souslov, A.J. Liu, T.C. Lubensky, Phys. Rev. Lett. 103, 205503 (2009)

    Article  ADS  Google Scholar 

  11. C.S. O'Hern, L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. E 68, 011306 (2003)

    Article  ADS  Google Scholar 

  12. L.E. Silbert, A.J. Liu, S.R. Nagel, Phys. Rev. Lett. 95, 098301 (2005)

    Article  ADS  Google Scholar 

  13. M. Wyart, S.R. Nagel, T.A. Witten, Europhys. Lett. 72, 486 (2005)

    Article  ADS  Google Scholar 

  14. Shi Wei Liu, Yang Yang Yang, Wen Shan Duan, Lei Yang, Phys. Rev. E 92, 013202 (2015)

    Article  ADS  Google Scholar 

  15. W.A. Allen, E.B. Mayfield, H.L. Morrison, J. Appl. Phys. 28, 370 (1957)

    Article  ADS  Google Scholar 

  16. M.J. Forrestal, V.K. Luk, Int. J. Impact Eng. 12, 427 (1992)

    Article  Google Scholar 

  17. K.A. Newhall, D.J. Durian, Phys. Rev. E 68, 060301(R) (2003)

    Article  ADS  Google Scholar 

  18. M.A. Ambroso, C.R. Santore, A.R. Abate, D.J. Durian, Phys. Rev. E 71, 051305 (2005)

    Article  ADS  Google Scholar 

  19. L. Tsimring, D. Volfson, in Proceedings of the International Conference on Powders and Grains, Vol. 2 (Taylor & Francis, London, 2005) pp. 1215--1223

  20. H. Katsuragi, D.J. Durian, Nat. Phys. 3, 420 (2007)

    Article  Google Scholar 

  21. D.I. Goldman, P. Umbanhowar, Phys. Rev. E 77, 021308 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  22. E.L. Nelson, H. Katsuragi, P. Mayor, D.J. Durian, Phys. Rev. Lett. 101, 068001 (2008)

    Article  ADS  Google Scholar 

  23. P. Umbanhowar, D.I. Goldman, Phys. Rev. E 82, 010301 (2010)

    Article  ADS  Google Scholar 

  24. Y. Takehara, S. Fujimoto, K. Okumura, EPL 92, 44003 (2010)

    Article  ADS  Google Scholar 

  25. A.H. Clark, L. Kondic, R.P. Behringer, Phys. Rev. Lett. 109, 238302 (2012)

    Article  ADS  Google Scholar 

  26. A.H. Clark, R.P. Behringer, EPL 101, 64001 (2013)

    Article  ADS  Google Scholar 

  27. A.H. Clark, L. Kondic, R.P. Behringer, in Proceedings of the International Conference on Powders and Grains, Vol. 1542 (AIP, Melville, New York, 2013) pp. 445--448

  28. M.P. Ciamarra, A.H. Lara, A.T. Lee, D.I. Goldman, I. Vishik, H.L. Swinney, Phys. Rev. Lett. 92, 194301 (2004)

    Article  ADS  Google Scholar 

  29. M.A. Ambroso, C.R. Santore, A.R. Abate, D.J. Durian, Phys. Rev. E 71, 051305 (2005)

    Article  ADS  Google Scholar 

  30. A.H. Clark, A.J. Petersen, R.P. Behringer, Phys. Rev. E 89, 012201 (2014)

    Article  ADS  Google Scholar 

  31. Alexandre Rosas, Daniel ben-Avraham, Katja Lindenberg, Phys. Rev. E 71, 032301 (2005)

    Article  ADS  Google Scholar 

  32. A. Rosas, K. Lindenberg, Phys. Rev. E 68, 041304 (2003)

    Article  ADS  Google Scholar 

  33. A.M. Walsh, K.E. Holloway, P. Habdas, J.R. de Bruyn, Phys. Rev. Lett. 91, 104301 (2003)

    Article  ADS  Google Scholar 

  34. E.L. Nelson, H. Katsuragi, P. Mayor, D.J. Durian, Phys. Rev. Lett. 101, 068001 (2008)

    Article  ADS  Google Scholar 

  35. M. Manciu, S. Sen, A.J. Hurd, Physica D 157, 226 (2001)

    Article  ADS  Google Scholar 

  36. G.E. Duvall, R. Manvi, S.C. Lowell, J. Appl. Phys. 40, 3771 (1969)

    Article  ADS  Google Scholar 

  37. E.B. Herbold, V.F. Nesterenko, Phys. Rev. E 75, 021304 (2007)

    Article  ADS  Google Scholar 

  38. Wen-Shan Duan, Zhen-Bin Zhang, Lei Yang, Phys. Rev. E 94, 052906 (2016)

    Article  ADS  Google Scholar 

  39. V.F. Nesterenko, Dynamics of Heterogeneous Materials (Springer-Verlag, New York, 2001)

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Authors and Affiliations

  1. College of Physics and Electronic Engineering, Northwest Normal University, 730070, Lanzhou, China

    Tao Liang, Yang Yang, Yu-Ren Shi, Juan-Fang Han & Wen-Shan Duan

  2. Key Laboratory of Marine Materials and Protective Technologies, Ningbo Institute and Engineering, Chinese Academy of Sciences, 315201, Ningbo, Zhejiang, China

    Xin Jiang

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  1. Tao Liang
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  2. Yang Yang
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  3. Yu-Ren Shi
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Correspondence to Tao Liang.

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Liang, T., Yang, Y., Shi, YR. et al. Shock wave due to the short-period impact in one-dimensional plasticity bead chain. Eur. Phys. J. E 41, 96 (2018). https://doi.org/10.1140/epje/i2018-11704-x

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