Bifurcation and Localization in Rate-Independent Materials. Some General Considerations

  • A. Benallal
  • R. Billardon
  • G. Geymonat
Part of the International Centre for Mechanical Sciences book series (CISM, volume 327)


This work deals with some aspects of bifurcation and localization phenomena for solids made of rate-independent materials. Only the theoretical developments are presented. Physical non-linearities (plasticity, damage, ...) and geometrical non-linearities are taken into account. The analysis is limited to quasi-static loadings. A full and complete analysis of the rate problem for incrementally linear solids is carried out. The first order rate problem is formulated and analysed in the framework of modern theory of linear elliptic boundary value problems. Three conditions are necessary and in the same time sufficient for this problem to be well-posed. These conditions are local in nature and are used to describe localization phenomena.


Fredholm Operator Kinematic Hardening Localization Phenomenon Ellipticity Condition Bifurcation Phenomenon 
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Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • A. Benallal
    • 1
  • R. Billardon
    • 1
  • G. Geymonat
    • 1
  1. 1.University of Paris 6Cachan CedexFrance

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