Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-25T15:12:36.513Z Has data issue: false hasContentIssue false
  • English
  • Français

Analogy Between the Groundstate of an Antiferromagnet and the Mode of Quasi-Static Deformation of a Packing of Spheres.

Published online by Cambridge University Press:  01 January 1992

P. Evesque
P. Evesque*
Affiliation:
Laboratoire de Mécanique: Sols-Structures-Matériaux, Ecole Centrale Paris, F-92295CHATENAY-MALABRY, FRANCE
Get access

Abstract

We report on local and global processes during the mechanical deformation of packings of spheres. We demonstrate that solid friction imposes a counter-rotation interaction to two adjacent grains during the deformation in order to minimize losses. This is equivalent to introduce an anti-ferromagnetic spin-like interaction in the structure; the search for the deformation process is quite similar to that one of finding the groundstate of an anti- ferromagnetic disordered structure with special boundary conditions. We demonstrate experimentally that boundaries may produce leading frustration processes; in this case, they govern most of the deformation mode and cancel mostly the influence of bulk mechanical properties (at least in the case when global “antiferromagnetic” order of the bulk is allowed by the absence of frustration). Frustration due to triangular local structure is described and existence of “anti-ferromagnetic-like” domains is proved; these domains are induced by the adequation between the boundary conditions and the deformation process and the domain wall is a stress-localization band as named in classical soil mechanics.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 291: Symposium O – Materials Theory and Modeling , 1992 , 97
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.a)Savage S.B., S.B. & Nohguchi, Y., Acta Mechanica 75, 153–174, (1988); b) Baxter, G.W., Behringer, R.P., Fagert, T.. and Johnson, G.A.. A., Phys. Rev. Lett. 62, 2825, (1989); BAXTER, G.W. and BEHRINGER, R.P., Phys. Rev. A42. 1017,(1990)Google Scholar
2. Schofield, A.N. & C.P. Wroth Critical State of Soil Mechanics, (Mac Graw Hill, London, 1968)Google Scholar
3. Collins, I.F., J. Mech. Phys. Solid 38, 1–25, (1990); ROWE P.W., Proc. Roy. Soc. Lndn A269, 500–527, (1962)Google Scholar
4. Evesque, P. and Stefani, C., J. Phys. II France 1, 1337–47, (1991)Google Scholar
5. Laroche, C., Douady, S. & Fauve, S., J. Phys. France, 50, 9–706, (1989); P. Evesque & J. Rajchenbach, Phys. Rev. Lett. 62 , 44, (1988); Savage, S.B., Fluid, J. Mech., 194, 457, (1988); Zik, O.. & Stavans, J., Europhys. Lett.Google Scholar
6. Evesque., P., J. Phys. France, 51, 697–700, (1990); Szmatula, E., Denis, J.-P., Evesque, P., Acad, C. R.. Sci. Paris, 310, série II, 1175–1178, (1990)Google Scholar
7. Evesque, P., Alfonsi, P., Stefani, C., Barbé, B., C.R. Acad. Sc. Paris, 311, série II, 393–398, (1990)Google Scholar
8. Bak, P., Tang, C., Wiesenfeld, K., Phys. Rev. Lett. 59, 381, (1987); and Phys. Rev. A38. 364, (1988)Google Scholar
9. Evesque, P. & Rajchenbach, J., C.R. Acad. Sc. (Paris) 307, Série II, 223, (1988); Jaëger, H.M., Liu, C.H., Nagel, S., Phys. Rev. Lett. 62, 40, (1989); Held, G.A., Solin, D.H., Kean, D.T., Horn, W.J., Grinstein, G., Phys. Rev. Lett. 65, 1120, (1990)Google Scholar
10. Evesque, P., J. Phys. France 51, 2515, (1990); Europh. Lett 14, 427, (1991); Phys. Rev. A43. 2720–40, (1991).Google Scholar
11. Bagnold, R.A., Proc. Roy. Soc. Lndn Ser. A225, 49 (1954) and ib. A295. 219 (1966)Google Scholar
12. Biarez, J. & P.-Y. Hicher, in “Powders and Grains“, ed. Biarez, J. & Gourvès, R;, (Balkema, Rotterdam, 1989), pp. 1–13; and in “Lois de Comportement des Sols Remaniés”, Cours de D.E. A. de Mécanique des Sols et Structures, Ecole Centrale Paris, 1989)Google Scholar
13. Cundall, P.A., Strack, O.D.L., in Mechanics of Granular Materials and Constitutive Relations, ed. Jenkins, J.T. & Satake, M., (Elsevier, Amsterdam, 1983), pp. 137–149; Campbell, C.S. and Brennen, L.N.., J. Fluid Mech. 151, 167, (1985); Y.M. Bashir & J.D. Goddard, J. Rheol. 35, 849-85, (1991) CundallGoogle Scholar
14. Evesque, P. submitted to publication; P. Evesque & D. Somette., to appear in the Proceedings of the International Conf. on Mechanics, Physics and Structure of Materials “A Celebration of Aristotle's 23 Centuries, in J. of the Mechanical Behavior of MaterialsGoogle Scholar
15. Binder, K. & Young., A.P., Rev. Mod. Phys. 58, 801–976, (1986); Mézard, M., Parisi, G. & Virasoro, M.A., Spin Glass Theory and Beyond. World Scientist Lecture Notes in Physics, vol.9. (1987)Google Scholar
16. Bray, A.J., Moore, M.A., Phys. Rev. Lett. 58, 57, (1987); ZHANG Y.C., Phys. Rev. Lett. 59, 2125–8, (1987)Google Scholar
17. Dantu, P., Géotechnique 18, 50–55, (1968); Annales des Ponts et Chaussées IV, 1–10, (1967)Google Scholar
18.accepted for publication in Acad, C.R.. Sciences Paris, France.Google Scholar