.. _V7.22.103:

**v7.22.103** HSNV103 - Thermoplasticity and metallurgy in plane deformations
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**Summary:**

We treat the determination of the mechanical evolution of a rectangular parallepiped in plane deformations subject to known and uniform thermal :math:`T(t)` and metallurgical :math:`Z(t)` evolutions (metallurgical transformation is of the bainitic type).

The elements used are two-dimensional elements in plane deformations and the behavioral relationship is von Mises plasticity with linear isotropic work hardening (for modellingB, transformation plasticity is also taken into account).

The elastic limit and the slope of the tensile curve depend on temperature and metallurgical composition.

The expansion coefficient :math:`\alpha` depends on the metallurgical composition.

For modeling A (without transformation plasticity), the reference solution is obtained by analytically solving the problem. For modeling B (with transformation plasticity), the reference solution is obtained by the numerical resolution of the problem using axisymmetric elements for which the condition of plane deformations is imposed.

The results provided by*Code_Aster* are very satisfactory with errors of less than 0.5%.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence__pour_la_mod_lisation_A_
    Mod_lisation_A
    R_sultats_de_la_mod_lisation_A
    Mod_lisation_B
    R_sultats_de_la_mod_lisation_B
    Synth_se_des_r_sultats