Generic Singularities for Plastic Instability Problems
Plastic instability is discussed from the point of view of generic bifurcation theory. We try to get an exhaustive classification of the singularities that can occur for the socalled dissipative systems. This goal is achieved for systems with two degrees
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BIFURCATION AND STABILITY OF DISSIPATIVE SYSTEMS
EDITEDBY Q.S. NGUYEN ECOLE POL YfECHNIQVE, PALAISEAU
SPRINGER-VERLAG WIEN GMBH
Le spese di stampa di questo volume sono in parte coperte da
contributi del Consiglio Nazionale delle Ricerche.
This volume contains 65 illustrations.
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concemed specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. © 1993 by Springer-Verlag Wien Originally published by Springer Verlag Wien-New York in 1993
In order to make this volume available as economically and as
rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-82437-5 DOI 10.1007/978-3-7091-2712-4
ISBN 978-3-7091-2712-4 (eBook)
PREFACE
This book contains six Ieerures delivered at the International Centre for Mechanical Sciences, Udine, ltaly in the session "Bifurcation and Stability of Dissipative Systems", June 1991. The first theme concerns the plastic buckling of structures in the spirit of Hill's classical approach. Non-bifurcation and stability criteria are introduced and postbifurcation analysis perforrned by asyrnptotic development method in relation with Hutchinson's work. Links with Koiter's elastic analysis are underlined. Some additional mathematical problems ofplastic bifurcation are discussed, in particular the possibility of smooth bifurcation is considered. Sorne recent results on the generalized Standardmodel are also given and their connection to Hill's general forrnulation is also be presented. Instability phenornena of inelastic jlow processes such as strain localization and necking are discussed in the same spirit. The second therne concerns stability and bifurcation problems in internally damaged or cracked solüJs. In brittle fracture or brittle damage, the evolution law of crack lenghts or damage parameters is time-independent like in plasticity and Ieads to a similar rnathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hili can be again obtained frorn the discussion of the rate response. The book is intendedfor post-graduate students, researchers and engineers who are interested in bifurcation and stability analysis in anelasticity and represents a selfconsistent treatise on plastic buckling with an unified presentation covering other Standard time-independent processes such as instability and bifurcation problerns in damage andfracture. Chapter 1, by A. Benallal, R. Billardon and J. Geymonat, gives some general considerations on bifurcation and localization in tirne-independent materials. Afull and complete analysis of the rate problern for incrernentallinear solid is carried out. The rate problern is formulated and discussed in the framework of the moder
