.. _V7.22.132:

**v7.22.132** HSNV132 - X-FEM crack in thermo-elasticity
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**Summary**

The purpose of this test is to validate the consideration of thermal loading for a cracking calculation by the X- FEM [:ref:`bib1 <bib1>`] method on an academic case :math:`\mathrm{2D}/\mathrm{3D}`.

This test involves a square plate with a straight through crack, embedded on the lower edge, and subjected to a horizontal temperature gradient. This loading has the effect of opening the crack. We compare the displacement for the end node at the top right, for FEM and X- FEM. This test includes a call to THER_LINEAIRE, then MECA_STATIQUE.

Four models are considered:


* modeling :math:`A`: :math:`\text{FEM}\mathrm{2D}` (taken as a reference),


* modeling :math:`B`: :math:`\text{X-FEM}\mathrm{2D}`, crack in the middle of the elements,


* modeling :math:`C`: :math:`\text{X-FEM}\mathrm{3D}` (we block the movements following :math:`z`), crack in the middle of the elements,


* modeling :math:`D`: :math:`\text{X-FEM}\mathrm{3D}`, real modeling :math:`\mathrm{3d}`, without putting :math:`\mathit{DZ}=0`, to validate the calculation of :math:`G` in :math:`\mathrm{3D}`.


* modeling :math:`E`: :math:`\text{X-FEM}\mathrm{3D}`, real modeling :math:`\mathrm{3d}`, without putting :math:`\mathrm{DZ}=0`, to validate the calculation of :math:`G` in :math:`\mathrm{3D}`. Similar to modeling :math:`D` except that the top and bottom surfaces have been embedded to induce significant stresses.

There is a gap of less than :math:`\text{1\%}` for travel, and a gap of :math:`\text{3,5\%}` over :math:`{K}_{I}` and :math:`\text{1,4 \%}` out of :math:`{K}_{\mathit{II}}`.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Mod_lisation_A___fissure_maill_e_en_dimension_2
    Mod_lisation_B___fissure_non-maill_e_en_dimension_2
    Mod_lisation_C___fissure_non-maill_e_en_faux_3D
    Mod_lisation_D___fissure_non-maill_e_en_vrai_3D
    Mod_lisation_E___fissure_non-maill_e_en_3D_avec_2_surfaces_encastr_es_
    Synth_ses_des_r_sultats