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.
This is a preview of subscription content, log in to check access.
Buy single article
Instant access to the full article PDF.
Price includes VAT for USA
Subscribe to journal
Immediate online access to all issues from 2019. Subscription will auto renew annually.
This is the net price. Taxes to be calculated in checkout.
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)
Mueth D.M., Jaeger H.M., Nagel S.R.: Force distribution in a granular medium. Phys. Rev. E 57(3), 3164–3169 (1998)
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)
Majmudar T.S., Behringer R.P.: Contact force measurements and stress-induced anisotropy in granular materials. Nature 435, 1079–1082 (2005)
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)
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)
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)
Socolar J.E.S.: Average stresses and force fluctuations in noncohesive granular materials. Phys. Rev. E 57(3), 3204–3215 (1998)
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)
Crowin E.I., Jaeger H.M., Nagel S.R.: Structural signature of jamming in granular media. Nature 435, 1075–1078 (2005)
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)
Liu C.h., Nagel S.R.: Sound and vibration in granular materials. J. Phys. Condens. Matter 6, A433–A436 (1994)
Jia X., Carol C., Velicky B.: Ultrasound propagation in externally stressed granular media. Phys. Rev. Lett. 82(9), 1863–1866 (1999)
Hostler S.R., Brennen C.E.: Pressure wave propagation in a granular bed. Phys. Rev. E 72, 031303 (2005)
Fukushima E.: Granular flow studies by nmr: a chronology. Adv. Complex Syst. 4(4), 503–507 (2001)
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)
Muthupillai R., Ehman R.L.: Magnetic resonance elastography. Nat. Med. 2(5), 601–603 (1996)
Lewa C.J.: Elasto-magnetic resonance spectroscopy. Europhys. Lett. 35(1), 73–76 (1996)
Blümich B.: NMR Imaging of Materials. Clarendon Press, Oxford (2000)
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)
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)
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)
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)
Louge M.Y., Tuozzolo C., Lorenz A.: On binary impacts of small liquid-filled shells. Phys. Fluids 9(12), 3670–3677 (1997)
About this article
Cite this article
Sanfratello, L., Fukushima, E. & Behringer, R.P. Using MR elastography to image the 3D force chain structure of a quasi-static granular assembly. Granular Matter 11, 1–6 (2009). https://doi.org/10.1007/s10035-008-0112-4
- Force chains
- MR elastography