.. _V7.22.102:

**v7.22.102** HSNV102 - Thermo-metallo-plasticity coupled with simple traction
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**Summary:**

We treat the determination of the mechanical evolution of a cylindrical bar subjected to known and uniform thermal :math:`T(t)` and metallurgical :math:`Z(t)` evolutions (the metallurgical transformation is of the martensitic type).

The elements used are axisymmetric elements.

For models A and B, the behavioral relationship is VonMises plasticity with isotropic work hardening. For modellingB, transformation plasticity is also taken into account.

In the C modeling, viscoplastic behavior with linear isotropic work hardening is considered and the transformation plasticity is not 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.

Metallurgical transformations take place at :math:`{\dot{\epsilon }}^{p}\ne 0` (this is in this sense that the test **couple** the transformation plasticity of classical plasticity).


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    R_sultats_de_la_mod_lisation_A
    Mod_lisation_B
    R_sultats_de_la_mod_lisation_B
    Mod_lisation_C
    R_sultats_de_la_mod_lisation_C
    Synth_se_des_r_sultats