Mode switching and recursive bifurcation in granular materials

Journal of the Mechanics and Physics of Solids

Volumn 45, Issue 11-12, 1997, Pages 1929-1953

  Ikeda, K ^a   Murota, K ^b   Yamakawa, Y ^a   Yanagisawa, E ^a  

^a TOHOKU UNIVERSITY   (Japan)

^b KYOTO UNIVERSITY   (Japan)

Author keywords

A. buckling; B. granular material; C. stability and bifurcation

Indexed keywords

BIFURCATION (MATHEMATICS); BUCKLING; DEFORMATION; GRANULAR MATERIALS; SENSITIVITY ANALYSIS; SHEAR STRESS;

MODE SWITCHING; RECURSIVE BIFURCATION;

COMPOSITE MICROMECHANICS;

EID: 0031270914     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(97)00020-3     Document Type: Article

References (26)

1. Asaoka, A. and Noda, T. (1995) Imperfection-sensitive bifurcation of Cam-clay under plane strain compression with undrained boundaries. Soils Foundations 35, 83-100.
2. Chambon, R., Desrues, J. and Vardoulakis, I. (1993) Localization and bifurcation theory for soils and rocks. Proceedings of the Third International Workshop on Localization and Bifurcation Theory for Soils and Rocks, Grenoble, France.
3. De Borst, R. (1988) Bifurcation in finite element models with non-associated flow law. Int. J. Numerical Analytical Methods Geomechanics 12, 99-116.
4. Dinkevich, S. (1991) Finite symmetric systems and their analysis. Int. J. Solids Structures 27, 1215-1253.
5. Golubitsky, M. and Schaeffer, D. G. (1985) Singularities and Groups in Bifurcation Theory 1. Springer, New York.
6. Golubitsky, M., Stewart, I. and Schaeffer, D. G. (1988) Singularities and Groups in Bifurcation Theory 2. Springer, New York.
7. Hartono, W. and Nishino, F. (1991) Imperfection behavior of elastic non-linear systems illustrated by a three-degree-of freedom model. AIAA J. 29, 1507-1514.
8. Hill, R. and Hutchinson, J. W. (1975) Bifurcation phenomena in the plane tension test. J. Mech. Phys. Solids 23, 239-264.
9. Ikeda, K. and Goto, S. (1993) Imperfection sensitivity for size effect of granular materials. Soils Foundations 33, 157-170.
10. Ikeda, K. and Murota, K. (1997a) Recursive bifurcation as sources of complexity in soil shearing behavior. Soils Foundations 37.
11. Ikeda, K. and Murota, K. (1997b) Systematic description of imperfection sensitive bifurcation behavior of symmetric systems. RIMS Preprint 114D, Kyoto University.
12. Ikeda, K., Chida, T. and Yanagisawa, E. (1997) Imperfection sensitive strength variation of soil specimens. J. Mech. Physics Solids 45(2), 293-315.
13. Ikeda, K., Murota, K. and Fujii, H. (1991) Bifurcation hierarchy of symmetric structures. Int. J. Solids Structures 27, 1551-1573.
14. Kettle, S. F. A. (1995) Symmetry and Structure, 2nd edition. Wiley.
15. Kodaka, T., Asaoka, A. and Suzuki, K. (1994) Shearing properties and failure pattern of sand specimens with initial imperfections. Proc. 49th Annual Conf. JSCE III-156, 306-307.
16. Koiter, W. T. (1945) On the stability of elastic equilibrium. Ph.D. dissertation, Delft, Holland (English translation: NASA Tech. Trans. F10: 833, 1967).
17. Koiter, W. T. (1945) On the stability of elastic equilibrium. Ph.D. dissertation, Delft, Holland (English translation: NASA Tech. Trans. F10: 833, 1967).
18. Murota, K. and Ikeda, K. (1991) Critical imperfection of symmetric structures. SIAM J. Appl. Math. 51, 1222-1254.
19. Needleman, A. and Tvergaard, V. (1984) Finite element analysis on location in plasticity. Special Problems in Solids Mech., ed. Oden and Carley, pp. 94-157. Prentice-Hall.
20. Ortiz, M., Leroy, Y. and Needleman, A. (1987) A finite element analysis for localized failure analysis. Comput. Methods in Appl. Mech. and Eng. 61, 189-214.
21. Palassopoulos, G. V. (1989) Optimization of imperfection-sensitive structures. J. of Engineering Mechanics, ASCE 115, 1663-1682.
22. Rudnicki, J. W. and Rice, J. R. (1975) Conditions for the localization of deformation in pressure-sensitive dilatant materials. J. Mech. Phys. Solids 23, 239-264.
23. Sattinger, D. H. (1979) Group theoretic methods in bifurcation theory. Lecture Notes in Mathematics 762. Springer.
24. Thompson, J. M. T. and Hunt, G. W. (1973) A General Theory of Elastic Stability. Wiley, London.
25. Vardoulakis, I. (1986) Stability and bifurcation in geomaterials. Numerical Methods in Geomechanics, ed. Swoboda, pp. 155-168. Balkema.
26. Yatomi, C., Yashima, A., Iizuka, A. and Sano, I. (1989) General theory of shear bands formation by a non-coaxial Cam-clay model. Soils Foundations 29, 41-53.