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On the Bifurcation and Postbifurcation Theory for a General Class of Elastic-Plastic Solids

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

Abstract

The present work is concerned with the bifurcation and postbifurcation analysis of a class of rate independent plasticity models obeying Hill’s maximum dissipation principle. A variational inequality approach, which differs from the classical formulation of the plastic bifurcation problem, is employed. The rate n bifurcation problem is formulated and sufficient conditions for uniqueness of the corresponding boundary value problem are given. A connection is made with Hill’s nonbifurcation criterion. In addition the issue of the postbifurcation behavior of the solid is addressed in this more general context showing the possiblity of angular as well as smooth bifurcations of rate n > 1.

Finally an example, capable of exhibiting both an angular as well as a smooth bifurcation is analyzed using the general formulation derived in this work. The presentation is concluded with some comments and comparisons of the present methodology with the classical approach.

Keywords

Variational Inequality Positive Definitness Bifurcation Problem Bifurcate Solution Plastic Solid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Wien 1993

Authors and Affiliations

  • N. Triantafyllidis
    • 1
  1. 1.The University of MichiganAnn ArborUSA

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