Bifurcation and Stability of Time-Independent Standard Dissipative Systems

  • Q. S. Nguyen
Part of the International Centre for Mechanical Sciences book series (CISM, volume 327)


This paper presents a general course on stability and bifurcation of dissipative systems based upon energetic considerations. For time-independent systems, it provides an unified framework for the study of quasi-static evolutions and of stability or bifurcation problems in a variety of interesting applications. The theoretical presentation is complemented by a number of simple analytical examples.

The first main issue to be addressed pertains to the buckling of elastic-plastic structures. Stability and bifurcation criteria are discussed for generalized standard models of plasticity in the light of Hill’s results.

The second main issue to be addressed pertains to the stability and bifurcation of systems with internal damage or cracks. In brittle fracture or brittle damage, the evolution law of crack lengths or of damage parameters is time-independent as in plasticity and leads to a similar mathematical description of the quasi-static evolution of these systems. Stability and bifurcation analysis can be performed in the same spirit.


Variational Inequality Elastic Stability Trivial Equilibrium Elastic Plastic Dissipative Potential 
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

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

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