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Structural Engineering and Mechanics
  Volume 16, Number 2, August 2003 , pages 141-152

Characteristics of solutions in softening plasticity and path criterion
G. Chen and G. Baker

    Characteristics of solutions of softening plasticity are discussed in this article. The localized and non-localized solutions are obtained for a three-bar truss and their stability is evaluated with the aid of the second-order work. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the second-order work exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the second-order work, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, it is proposed that the structure should follow the path corresponding to the absolute minimum point of the second-order work. The proposal is further proved equivalent to Bazant\'s path criterion derived on a thermodynamics basis.
Key Words
    softening plasticity; strain localization; bifurcation; energy minimization; path criterion.
Faculty of Engineering & Surveying, The University of Southern Queensland,
Toowoomba, QLD 4350, Australia

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