Energy profile and bifurcation analysis in softening plasticity

Chen, G. and Baker, Graham (2004) Energy profile and bifurcation analysis in softening plasticity. Advances in Structural Engineering, 7 (6). pp. 515-523. ISSN 1369-4332

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Bifurcations of solutions and energy profile in softening plasticity are discussed in this paper. The localized and non-localized solutions are obtained for a simple softening bar; the second-order derivatives of the incremental energy are evaluated. The second-order derivatives along the fundamental path demonstrate a discontinuity at the bifurcation point; the eigen-analysis of the tangential stiffness matrix fails to identify the post-bifurcation paths. The energy variation near the bifurcation point is investigated; the relationship between the stationary points of the energy profile and post-bifurcation solutions is established. Beyond the bifurcation point, the single stable loading path splits into several post-bifurcation paths and the incremental energy exhibits several competing minima. Among the multiple post-bifurcation equilibrium states, the localized solutions correspond to the minimum points of the energy profile, while the non-localized solutions correspond to the saddles and local maximum points. To determine the real post-bifurcation path, the concept of minimization of the second-order energy is used as the criterion for the bifurcation analysis involved in softening plasticity. As an application, a lattice model of a beam is analyzed and damage localization is obtained.

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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Electronic version unavailable.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering
Date Deposited: 06 May 2010 12:14
Last Modified: 16 Nov 2011 04:39
Uncontrolled Keywords: bifurcation analysis; energy profile; multiple equilibrium states; softening plasticity; strain localization; boundary conditions; deformation; eigenvalues and eigenfunctions
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis
09 Engineering > 0905 Civil Engineering > 090599 Civil Engineering not elsewhere classified
Socio-Economic Objective: B Economic Development > 87 Construction > 8703 Construction Materials Performance and Processes > 870301 Cement and Concrete Materials
Identification Number or DOI: 10.1260/1369433042863224

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