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http://dx.doi.org/10.12989/sem.2003.16.2.141

Characteristics of solutions in softening plasticity and path criterion  

Chen, G. (Faculty of Engineering & Surveying, The University of Southern Queensland)
Baker, G. (Faculty of Engineering & Surveying, The University of Southern Queensland)
Publication Information
Structural Engineering and Mechanics / v.16, no.2, 2003 , pp. 141-152 More about this Journal
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.
Keywords
softening plasticity; strain localization; bifurcation; energy minimization; path criterion;
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