Equilibrium and Stability of Elastic-plastic Bodies

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


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
$$\psi (\sigma ) \leqslant 0$$
(Von Mises [9]). Stresses are determined by the elastic strains
$$\sigma ij = {A_{ijkl}}{\gamma _{kl}}$$
The total strain ε ij ,
$${\varepsilon _{ij}} = {\gamma _{ij}} + {\alpha _{ij}}$$
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.


Plastic Strain Elastic Strain Reference Position Virtual Displacement Lagrangean Strain 
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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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