.. _r5.03.02:

**r5.03.02** Integration of Von Mises elasto-plastic behavior relationships
====

**Summary**:

This document describes the quantities calculated by the operator STAT_NON_LINE necessary for the implementation of the quasistatic nonlinear algorithm described in [:ref:`R5.03.01 <R5.03.01>`] in the case of elasto-plastic behaviors. These quantities are calculated by the same subprograms in the operator DYNA_NON_LINE in the case of a dynamic load [:ref:`R5.05.05 <R5.05.05>`].

This description is presented according to the various keywords that allow the user to choose the desired behavioral relationship. The behavioral relationships covered here are:


*   the Von Mises behavior under isotropic work hardening (linear or non-linear)


*   the Von Mises behavior with linear kinematic work hardening (Prager model)

The integration method used is based on a direct implicit formulation. From the initial state, or from the previous calculation instant, the stress field resulting from a deformation increment is calculated. The tangent operator is also calculated.




.. toctree::
    :hidden:

    self

.. toctree::
    :maxdepth: 2
    :numbered:

    Introduction
    Notations_g_n_rales_et_hypoth_ses_sur_les_d_formations
    Relation_de_von_Mises____crouissage_isotrope
    Relation_de_Von_Mises____crouissage_cin_matique_lin_aire
    Bibliographie