Computation of large strains associated with plastic instability of in-plane loaded plates

A. H. Elkholy, M. A. Karkoub, O. M. Al-Hawaj

Research output: Contribution to journalArticle


In the elastic-plastic deformation of solids, which exhibit pronounced large strains, readily detectable cavities occur in critical zones, which lead eventually to failure by rupture. In this study, a modified form of constitutive equation for elastic-plastic deformation of solids is proposed. The form takes into consideration the effect of rotation of various principal axes during the process of continued deformation. Bifurcation analysis of rectangular plates that are subjected to biaxial loading is carried out to determine bifurcation stresses at the onset of cavity formation. Both symmetric and antisymmetric modes of bifurcation are determined. We found that the modified relation leads to bifurcation stresses, which are lower than those, obtained when the classical Prandtl-Reuss relation is used, and therefore, are comparable with the results obtained experimentally.

Original languageEnglish
Pages (from-to)11-20
Number of pages10
JournalModelling, Measurement and Control B
Issue number3-4
Publication statusPublished - 1 Dec 2005



  • Bifurcation
  • Elastic-plastic
  • Modes of deformation
  • Plates

ASJC Scopus subject areas

  • Modelling and Simulation
  • Condensed Matter Physics
  • Mechanical Engineering
  • Computer Science Applications

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