Abstract
The conditions for the localization of the deformation in rate-independent materials, understood as a first order bifurcation, are obtained by the analysis of the rate problem. Three types of localization phenomena are exhibited from this analysis: the deformation may localize inside the body, at its boundaries or at its possible interfaces. The corresponding conditions are given mechanical interpretations and used as indicators of local rupture of the material.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
J. Hadamard, Lecons sur la propagation des ondes et les équations de l’hydrodynamique (Paris, 1903).
R. Hill, J. Mech. Phys. Solids, 10, 1–16 (1962).
J. Mandel, J. de Mécanique, 1, 3–30 (1962).
J.R. Rice in Theoretical and Applied Mechanics, 207–220, edited by W.T. Koiter (North-Holland, 1976).
A. Benallal, R. Billardon & G. Geymonat in Cracking and Damage, 247–258, edited by J. Mazars & Z.P. Bazant (Elsevier, 1989).
A. Benallal, R. Billardon & G. Geymonat, C.R. Acad. Sci. Paris, 308. (II), 893–898 (1989).
A. Benallal, R. Billardon & G. Geymonat, in Actes Congrès Francais de Mécanique, 1, 242–243 (AUM, Metz 1989).
A. Benallal, R. Billardon & G. Geymonat, C.R. Acad. Sci. Paris, 310 (II), 679–684 (1990).
A. Benallal, R. Billardon & G. Geymonat, Constitutive Laws for Engineering Materials, 387–390, edited by C.S. Desai & G. Frantziskonis (Elsevier, 1991).
R. Billardon & I. Doghri, C. R. Acad. Sci. Paris, 308 (II), 347–352 (1989).
G. Borre & G. Maier, Meccanica, 24, 36–41 (1989).
J. Rudnicki & J.R. Rice, J. Mech. Phys. Solids, 23, 371–394 (1975).
J. Rudnicki & J.R. Rice, Int. J. Solids Struct., 16, 597–605 (1980).
A. Benallal & R. Billardon, Internal report, LMT-Cachan (1991).
A. Benallal, D. Boudon & E. Lajoix, Internal report, LMT-Cachan (1991).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Elsevier Science Publishers Ltd
About this paper
Cite this paper
Benallal, A., Billardon, R. (1991). Hierarchy of Localization Phenomena Inside, at the Boundaries and Interfaces of Solids. In: Boehler, JP., Khan, A.S. (eds) Anisotropy and Localization of Plastic Deformation. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3644-0_9
Download citation
DOI: https://doi.org/10.1007/978-94-011-3644-0_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-85166-688-1
Online ISBN: 978-94-011-3644-0
eBook Packages: Springer Book Archive