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Dynamics of oblique impact in a quasi two-dimensional granular medium

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Abstract

When a solid projectile impacts a granular target, it experiences a drag force and abruptly comes to rest as its momentum transfers to the grains. An empirical drag force law successfully describes the force experienced by the projectile, and the corresponding grain-scale mechanisms have been deciphered for normal impacts. However, there is little work exploring non-normal impacts. Accordingly, we extend studies to explore oblique impact, in which a significant horizontal component of the drag force is present. In our experiments, a projectile impacts a quasi-two-dimensional bed of bidisperse photoelastic grains. We use high-speed imaging to measure high-resolution position data of the projectile trajectory and simultaneously visualize particle-scale force propagation in the granular medium. When the impact angle becomes important, the spatial structure of the stress response reveals relatively weak force chain propagation in the horizontal direction. Based on these observations, we describe the decrease of the inertial drag force with impact angle.

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References

  1. Katsuragi, Hiroaki: Physics of Soft Impact and Cratering. Springer, Tokyo (2016)

    Book  Google Scholar 

  2. Van Der Meer, Devaraj: Impact on granular beds. Annu. Rev. Fluid Mech. 49, 463–484 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  3. Li, Chen, Zhang, Tingnan, Goldman, Daniel: A terradynamics of legged locomotion on granular media. Science 339, 1408–1411 (2013)

    Article  ADS  Google Scholar 

  4. Daniels, K.E., Coppock, J.E., Behringer, R.P.: Dynamics of meteor impacts. Chaos Interdiscip. J. Nonlinear Sci. 14(4), S4–S4 (2004)

    Article  Google Scholar 

  5. Brzinski, T., Mayor, P., Durian, D.J.: Depth-dependent resistance of granular media to vertical penetration. PRL 111(168002), 168002 (2013)

    Article  ADS  Google Scholar 

  6. Tsimring, L., Volfson, D.: Modeling of impact cratering in granular media. Powders Grains 2, 1215–1223 (2005)

    Google Scholar 

  7. Zheng, Hu, Wang, Dong, Chen, David Z., Wang, Meimei, Behringer, Robert P.: Intruder friction effects on granular impact dynamics. Phys. Rev. E 98, 032904 (2018)

    Article  ADS  Google Scholar 

  8. Wada, Koji, Senshu, Hiroki, Matsui, Takafumi: Numerical simulation of impact cratering on granular material. Icarus 180(2), 528–545 (2006)

    Article  ADS  Google Scholar 

  9. Goldman, Daniel, Umbanhowar, Paul: Scaling and dynamics of sphere and disk impact into granular media. Phys. Rev. E 77(021308), 021308 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  10. Poncelet, J.V.: Cours de Mecanique Industrielle. Lithographie de Clouet, Paris (1829)

    Google Scholar 

  11. Katsuragi, Hiroaki, Durian, Douglas: Unified force law for granular impact cratering. Nat. Phys. 3(420), 420–422 (2007)

    Article  Google Scholar 

  12. Clark, Abram, Kondic, Lou, Behringer, Robert P.: Particle scale dynamics in granular impact. Phys. Rev. Lett. 109(238302), 238302 (2012)

    Article  ADS  Google Scholar 

  13. Cacey Stevens, Bester, Robert P, Behringer: Collisional model of energy dissipation in three-dimensional granular impact. Phys. Rev. E 95, 032906 (2017)

    Article  Google Scholar 

  14. Takehara, Y., Fujimoto, S., Okumura, K.: High-velocity drag friction in dense granular media. EPL 92(44003), 44003 (2010)

    Article  ADS  Google Scholar 

  15. Clark, Abram H., Petersen, Alec J., Behringer, Robert P.: Collisional model for granular impact dynamics. Phys. Rev. E 89, 012201 (2014)

    Article  ADS  Google Scholar 

  16. Misbah, C., Valance, A.: Sand ripple dynamics in the case of out-of-equilibrium aeolian regimes. Eur. Phys. J. E 12(4), 523–529 (2003)

    Article  Google Scholar 

  17. Wang, Dengming, Ye, Xiaoyan, Zheng, Xiaojing: The scaling and dynamics of a projectile obliquely impacting a granular medium. Eur. Phys. J. E 35(1), 7 (2012)

    Article  Google Scholar 

  18. Ye, Xiaoyan, Wang, Dengming, Zheng, Xiaojing: Effects of density ratio and diameter ratio on penetration of rotation projectile obliquely impacting a granular medium. Eng. Comput. 32(4), 1025–1040 (2015)

    Article  Google Scholar 

  19. Ye, Xiaoyan, Wang, Dengming, Zheng, Xiaojing: Influence of particle rotation on the oblique penetration in granular media. Phys. Rev. E 86(6), 061304 (2012)

    Article  ADS  Google Scholar 

  20. Alshanti, Waseem G., Alshanti, Ahmad G.: Linear and non-linear trajectories of oblique penetration into a granular system. Appl. Math. Inf. Sci. 11(3), 851–855 (2017)

    Article  Google Scholar 

  21. Clark, Abram H., Behringer, Robert P.: Granular impact model as an energy-depth relation. EPL 101(64001), 64001 (2013)

    Article  ADS  Google Scholar 

  22. Nelson, E., Katsuragi, H., Mayor, P., Durian, D.: Projectile interactions in granular impact cratering. Phys. Rev. Lett. 101(6), 068001 (2008)

    Article  ADS  Google Scholar 

  23. Seguin, A., Bertho, Y., Gondret, P.: Influence of confinement on granular penetration by impact. Phys. Rev. E 78(010301), 010301 (2008)

    Article  ADS  Google Scholar 

  24. Lesniewska, D., Muir Wood, D.: Photoelastic and photographic study of a granular material. Geotechnique 61(7), 605–611 (2011)

    Article  Google Scholar 

  25. Daniels, Karen, Kollmer, Jonathan, Puckett, James: Photoelastic force measurements in granular materials. Rev. Sci. Instrum. 88(5), 051808 (2017)

    Article  ADS  Google Scholar 

  26. Zheng, Hu, Wang, Dong, Barés, Jonathan, Behringer, Robert P: Sinking in a bed of grains activated by shearing. Phys. Rev. E 98(1), 010901 (2018)

    Article  ADS  Google Scholar 

  27. Ambroso, M.A., Kamien, R.D., Durian, D.J.: Dynamics of shallow impact cratering. Phys. Rev. E 72(041305), 041305 (2005)

    Article  ADS  Google Scholar 

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Acknowledgements

This work is dedicated to Prof. Robert Behringer, whom we are deeply indebted to and will forever miss. His role in supporting and mentoring this research clearly justifies inclusion as a coauthor. This work was funded by NSF Grant No. DMR1206351 and DMR1809762, ARO No. W911NF-18-1-0184, NASA Grant No. NNX15AD38G, the William M. Keck Foundation, and a Duke University Provost’s Postdoctoral fellowship (CSB).

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Correspondence to Cacey Stevens Bester.

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This article is part of the Topical Collection: In Memoriam of Robert P. Behringer.

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Bester, C.S., Cox, N., Zheng, H. et al. Dynamics of oblique impact in a quasi two-dimensional granular medium. Granular Matter 22, 51 (2020). https://doi.org/10.1007/s10035-020-01019-9

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