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
Full text not available from this repository.Abstract
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/School / Institute/Centre: | Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering (Up to 30 Jun 2013) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Engineering and Surveying - Department of Agricultural, Civil and Environmental Engineering (Up to 30 Jun 2013) |
| 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 (2008): | 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010301 Numerical Analysis 09 Engineering > 0905 Civil Engineering > 090599 Civil Engineering not elsewhere classified |
| Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490302 Numerical analysis 40 ENGINEERING > 4005 Civil engineering > 400599 Civil engineering not elsewhere classified |
| Socio-Economic Objectives (2008): | B Economic Development > 87 Construction > 8703 Construction Materials Performance and Processes > 870301 Cement and Concrete Materials |
| Identification Number or DOI: | https://doi.org/10.1260/1369433042863224 |
| URI: | http://eprints.usq.edu.au/id/eprint/7958 |
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