.. _V3.02.320:

**v3.02.320** SSLP320 - Propagation of an X-FEM through crack solicited in Mode I
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**Summary**

The purpose of this test is to validate the calculation of the stress intensity factors (:math:`{K}_{I}` and :math:`{K}_{\mathrm{II}}`) and the crack propagation path with X- FEM in 2D, in the context of linear elasticity.

This test involves a rectangular plate with an through crack, and subjected to a loading of traction on the lower and upper edges of the plate.

Three methods for managing the propagation of an X- FEM crack are available. Each of them is the subject of modeling.

Three models are considered:


* modeling A: mesh method,


* B modeling: simplex method,


* C modeling: upwind method,


* D modeling: geometric method,

The relevance of the results is evaluated by comparing the stress intensity factors with the analytical values.

We find a theoretical difference between :math:`{K}_{I}` and :math:`{K}_{I}` of less than 1.13% for the mesh method, 1.12% for the simplex method, 1.13% for the upwind method, 1.1% for the geometric method and 1.1% for the upwind & FMM method.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Solution_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Synth_ses_des_r_sultats