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

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

Research output: Contribution to journalArticle

Abstract

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
Volume74
Issue number3-4
Publication statusPublished - 2005
Externally publishedYes

Fingerprint

Large Strain
elastic deformation
Elastic deformation
plastic deformation
Plastics
Plastic deformation
plastics
Bifurcation
Elastic Deformation
Plastic Deformation
rectangular plates
cavities
Cavity
constitutive equations
Constitutive equations
Rectangular Plate
Biaxial
Rupture
Antisymmetric
Bifurcation Analysis

Keywords

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

ASJC Scopus subject areas

  • Software
  • Applied Mathematics

Cite this

Computation of large strains associated with plastic instability of in-plane loaded plates. / Elkholy, A. H.; Karkoub, Mansour; Al-Hawaj, O. M.

In: Modelling, Measurement and Control B, Vol. 74, No. 3-4, 2005, p. 11-20.

Research output: Contribution to journalArticle

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