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Equilibrium and Stability of Elastic-plastic Bodies

  • J. Christoffersen
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)

Abstract

The existence of a yield-surface in stress-space, is generally taken to be the most fundamental feature of elastic-plastic materials. This means that stresses σ ij a satisfy a yield-condition
$$\psi (\sigma ) \leqslant 0$$
(1.01)
(Von Mises [9]). Stresses are determined by the elastic strains
$$\sigma ij = {A_{ijkl}}{\gamma _{kl}}$$
(1.02)
The total strain ε ij ,
$${\varepsilon _{ij}} = {\gamma _{ij}} + {\alpha _{ij}}$$
(1.03)
is the sum of elastic strains and plastic strains α ij , The plastic strain is assumed to be constant when the inequality sign applies in (1.01), whereas for ψ (σ) = 0 the increment of α ij is determined so as to insure that an inadmissible state of stress will not occur.

Keywords

Plastic Strain Elastic Strain Reference Position Virtual Displacement Lagrangean Strain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag, Berlin/Heidelberg 1971

Authors and Affiliations

  • J. Christoffersen
    • 1
  1. 1.Technical University of DenmarkCopenhagenDenmark

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