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

Published online by Cambridge University Press:  01 January 1992

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

Research Article
Copyright © Materials Research Society 1993

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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, 591648 (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, 19771988);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