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Structural Engineering and Mechanics
  Volume 16, Number 2, August 2003, pages 141-152
DOI: http://dx.doi.org/10.12989/sem.2003.16.2.141
 


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

 
Abstract
    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.
 
Address
Faculty of Engineering & Surveying, The University of Southern Queensland,
Toowoomba, QLD 4350, Australia
 

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