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Bifurcation and Stability of Dissipative Systems

  • Q. S. Nguyen

Part of the International Centre for Mechanical Sciences book series (CISM, volume 327)

About this book

Introduction

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 post-bifurcation analysis performed by asymptotic development method in relation with Hutchinson’s work. Some recent results on the generalized standard model are given and their connection to Hill’s general formulation is presented. Instability phenomena of inelastic flow processes such as strain localization and necking are discussed. The second theme concerns stability and bifurcation problems in internally damaged or cracked colids. In brittle fracture or brittle damage, the evolution law of crack lengths or damage parameters is time-independent like in plasticity and leads to a similar mathematical description of the quasi-static evolution. Stability and non-bifurcation criteria in the sense of Hill can be again obtained from the discussion of the rate response.

Keywords

damage development flow fracture instability plasticity stability

Editors and affiliations

  • Q. S. Nguyen
    • 1
  1. 1.Ecole PolytechniquePalaiseauFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-7091-2712-4
  • Copyright Information CISM Udine 1993
  • Publisher Name Springer, Vienna
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-211-82437-5
  • Online ISBN 978-3-7091-2712-4
  • Series Print ISSN 0254-1971
  • Series Online ISSN 2309-3706
  • Buy this book on publisher's site
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