Hostname: page-component-745bb68f8f-mzp66 Total loading time: 0 Render date: 2025-02-04T18:43:24.032Z Has data issue: false hasContentIssue false
  • English
  • Français

A Dynamical System Theory of Large Deformations and Patterns in Non-Cohesive Solids

Published online by Cambridge University Press:  01 January 1992

Pierre Evesque  and
Didier Sornette
Pierre Evesque
Affiliation:
Laboratoire de Mécanique :Sols, Structures et Matériaux, CNRS URA 850, Ecole Centrale de Paris, 92295 Chatenay-Malabry Cedex, France
Didier Sornette
Affiliation:
Laboratoire de Physique de la Matière Condensée, URA CNRS 190, Université de Nice- Sophia Antipolis, Parc Valrose, 06034 NICE Cedex, France
Get access

Abstract

We propose a dynamical system theory of triaxial-test deformationS and localization bifurcation in brittle media. We apply it to predict that localization may occur in a packing looser than “critical” and that the general localization shape is a spiral staircase in axisymmetric 3-D cells. These two facts have recently been confirmed experimentally. This theory provides a framework for understanding the development of complex deformation patterns from the mechanics of localization and rupture.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 291: Symposium O – Materials Theory and Modeling , 1992 , 449
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. Sornette, A., Davy, P. and Sornette, D., Phys.Rev.Lett. 67, 2266 (1990). Sornette D., “Self-organized criticality in plate tectonics”, in the Proceeding of the NATO ASI “Spontaneous formation of space-time structures and criticality” Geilo, Norway 2-12 april 1991, edited by T. Riste and D. Sherrington, Kluwer Academic PublishersGoogle Scholar
2. Biarez, J. and Hicher, P.Y., in Powders and grains, ed. by Biarez, J. and Gourves, G., (Balkema, Rotterdam 1989), p.l; Brown, R.L. and Richard, J.C., Principles of Powder Mechanics. (Pergamon press, Oxford, U.K.), 1966 Google Scholar
3. Evesque, P. and Stefani, C., de Physique II, J., (Nov. 91) & C.R.Acad.Sciences (France) 312. Serie 1, 581 (1991)Google Scholar
4. Mermin, N.D., Rev.Mod.Phys. 51, 591–648 (1979)Google Scholar
5. Desrues, J., Mokni, M. and Mazerolle, F., Tomodensitometry and localization in sands, X Europ. Conf. on Soil Mech. and Found. Engin., Florence, May 1991ed. by the Italian Commitee on Soil Mech.. Google Scholar
6. Bergé, P., Pomeau, Y. and Vidal, C., Chaos, Order within, Wiley, John, New York (1984)Google Scholar
7. Coullet, P., Emilsson, K.P. and Plaza, F., Qualitative theory of defects in non-equilibrium systems, to appear (1991)Google Scholar
8. Haken, H., Springer Series in Synergetics, (Series ed.) (Berlin: Springer, 1977–1988);Synergetics : an overview, Rep.Prog.Phys. 52 515-553 (1989). P. Bak, C. Tang and K. Wiesenfeld, Phys.Rev.Lett.,52, 381-384, (1987); Phys.Rev. A38, 364 (1988)Google Scholar