Advertisement

Granular Matter

, Volume 11, Issue 1, pp 1–6 | Cite as

Using MR elastography to image the 3D force chain structure of a quasi-static granular assembly

  • Lori SanfratelloEmail author
  • Eiichi Fukushima
  • Robert P. Behringer
Article

Abstract

We have developed a magnetic resonance elastography (MRE) technique to experimentally investigate the force chain structure within a densely packed 3D granular assembly. MRE is an MRI technique whereby small periodic displacements within an elastic material are measured. We verified our MRE technique using a gel phantom and then extended the method to image the force carrying chain structure within a 3D granular assembly of particles under an initial pre-stressed condition, on top of which is superimposed a small-amplitude vibration. We find that significant coherent displacements form along force chains, where spin phase accumulates preferentially, allowing visualization. This work represents the first time that the internal force chain structure of a dry assembly of granular solids has been fully acquired in three dimensions.

Keywords

Force chains MR elastography MRI Granular 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Travers T., Ammi M., Bideau D., Gervois A., Messager J.C., Troadec J.P.: Uniaxial compression of 2d packings of cylinders. Effects of weak disorder. Europhys. Lett. 4, 329–332 (1987)CrossRefADSGoogle Scholar
  2. 2.
    Mueth D.M., Jaeger H.M., Nagel S.R.: Force distribution in a granular medium. Phys. Rev. E 57(3), 3164–3169 (1998)CrossRefADSGoogle Scholar
  3. 3.
    Sugano T., Miyata M., Tanaka T., Nakagawa M., Mustoe G.G.W., Kozawa D.: Experimental study on the force support system within a rubble rock foundation. In: Kishino, Y. (eds) Powders and Grains 2001, pp. 263–266. Swets and Zeitlinger, Lisse (2001)Google Scholar
  4. 4.
    Majmudar T.S., Behringer R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)CrossRefADSGoogle Scholar
  5. 5.
    Liu C.h., Nagel S.R., Schecter D.A., Coppersmith S.N., Majumdar S., Narayan O., Witten T.A.: Force fluctuations in bead packs. Science 269, 513–515 (1995)CrossRefADSGoogle Scholar
  6. 6.
    Coppersmith S.N., Liu C.h., Majumdar S., Narayan O., Witten T.A.: Model for force fluctuations in bead packs. Phys. Rev. E 53(5), 4673–4685 (1996)CrossRefADSGoogle Scholar
  7. 7.
    Radjai F., Jean M., Moreau J.-J., Roux S.: Force distributions in dense two-dimensional granular systems. Phys. Rev. Lett. 77(2), 274–277 (1996)CrossRefADSGoogle Scholar
  8. 8.
    Socolar J.E.S.: Average stresses and force fluctuations in noncohesive granular materials. Phys. Rev. E 57(3), 3204–3215 (1998)CrossRefADSMathSciNetGoogle Scholar
  9. 9.
    Miyata M., Sugano T., Tanaka T., Nakagawa M., Mustoe G.G.W., Kozawa D.: Study on the force support system within a rubble rock foundation. In: Kishino, Y. (eds) Powders and Grains 2001, pp. 267–270. Swets and Zeitlinger, Lisse (2001)Google Scholar
  10. 10.
    Crowin E.I., Jaeger H.M., Nagel S.R.: Structural signature of jamming in granular media. Nature 435, 1075–1078 (2005)CrossRefADSGoogle Scholar
  11. 11.
    Zhou J., Long S., Wang Q., Dinsmore A.D.: Meaurement of forces inside a three-dimensional pile of frictionless droplets. Science 312, 1631–1633 (2006)CrossRefADSGoogle Scholar
  12. 12.
    Liu C.h., Nagel S.R.: Sound and vibration in granular materials. J. Phys. Condens. Matter 6, A433–A436 (1994)CrossRefADSGoogle Scholar
  13. 13.
    Jia X., Carol C., Velicky B.: Ultrasound propagation in externally stressed granular media. Phys. Rev. Lett. 82(9), 1863–1866 (1999)CrossRefADSGoogle Scholar
  14. 14.
    Hostler S.R., Brennen C.E.: Pressure wave propagation in a granular bed. Phys. Rev. E 72, 031303 (2005)CrossRefADSMathSciNetGoogle Scholar
  15. 15.
    Fukushima E.: Granular flow studies by nmr: a chronology. Adv. Complex Syst. 4(4), 503–507 (2001)CrossRefGoogle Scholar
  16. 16.
    Muthupillai R., Lomas D.J., Rossman P.J., Greenleaf J.F., Manduca A., Ehman R.L.: Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 269, 1854–1857 (1995)CrossRefADSGoogle Scholar
  17. 17.
    Muthupillai R., Ehman R.L.: Magnetic resonance elastography. Nat. Med. 2(5), 601–603 (1996)CrossRefGoogle Scholar
  18. 18.
    Lewa C.J.: Elasto-magnetic resonance spectroscopy. Europhys. Lett. 35(1), 73–76 (1996)CrossRefADSGoogle Scholar
  19. 19.
    Blümich B.: NMR Imaging of Materials. Clarendon Press, Oxford (2000)Google Scholar
  20. 20.
    Venkatesh S.K., Yin M., Glockner J.F., Takahashi N., Araoz P.A., Talwalkar J.A., Ehman R.L.: MR elastography of liver tumors: preliminary results. Am. J. Roentgenol. 190, 1534–1540 (2008)CrossRefGoogle Scholar
  21. 21.
    Plewes D.B., Bishop J., Samani A., Sciarretta J.: Visualization and quantification of breast cancer biomechanical properties with magnetic resonance elastography. Phys. Med. Biol. 45, 1591–1610 (2000)CrossRefGoogle Scholar
  22. 22.
    McKnight A.L., Kugel J.L., Rossman P.J., Manduca A., Hartmann L.C., Ehman R.L.: MR elastography of breast cancer: preliminary results. Am. J. Roentgenol. 178(6), 1411–1417 (2002)Google Scholar
  23. 23.
    Jenkyn T.R., Ehman R.L., An K.-N.: Noninvasive muscle tension measurement using the novel technique of magnetic resonance elastography (mre). J. Biomech. 36, 1917–1921 (2003)CrossRefGoogle Scholar
  24. 24.
    Louge M.Y., Tuozzolo C., Lorenz A.: On binary impacts of small liquid-filled shells. Phys. Fluids 9(12), 3670–3677 (1997)CrossRefADSGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Lori Sanfratello
    • 1
    Email author
  • Eiichi Fukushima
    • 2
  • Robert P. Behringer
    • 3
  1. 1.New Mexico ResonanceAlbuquerqueUSA
  2. 2.ABQMRAlbuquerqueUSA
  3. 3.Department of PhysicsDuke UniversityDurhamUSA

Personalised recommendations