Energy profile and bifurcation analysis in softening plasticity
Article
Article Title | Energy profile and bifurcation analysis in softening plasticity |
---|---|
ERA Journal ID | 4147 |
Article Category | Article |
Authors | Chen, G. (Author) and Baker, Graham (Author) |
Journal Title | Advances in Structural Engineering: an international journal |
Journal Citation | 7 (6), pp. 515-523 |
Number of Pages | 9 |
Year | 2004 |
Publisher | SAGE Publications Ltd |
Place of Publication | Brentwood, Essex, UK |
ISSN | 1369-4332 |
2048-4011 | |
Digital Object Identifier (DOI) | https://doi.org/10.1260/1369433042863224 |
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. |
Keywords | bifurcation analysis; energy profile; multiple equilibrium states; softening plasticity; strain localization; boundary conditions; deformation; eigenvalues and eigenfunctions |
ANZSRC Field of Research 2020 | 490302. Numerical analysis |
400599. Civil engineering not elsewhere classified | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | Faculty of Engineering and Surveying |
https://research.usq.edu.au/item/9zx53/energy-profile-and-bifurcation-analysis-in-softening-plasticity
1780
total views0
total downloads8
views this month0
downloads this month