.. _V6.03.138:

**v6.03.138** SSNP138 - 2D angled crack with X- FEM
=========================================================

**Summary**

The purpose of this test is to validate the calculation of stress intensity factors (:math:`{K}_{I}` and :math:`{K}_{\mathit{II}}`) with :math:`\text{X-FEM}` [:ref:`bib1 <bib1>`] in :math:`\mathrm{2D}`, in the context of linear elasticity. This test also aims to test the volume loads of FORCE_INTERNE and PESANTEUR with the :math:`\text{X-FEM}` in :math:`\mathrm{2D}` method.

This test involves a rectangular plate with an inclined right central crack, and subjected to a tensile load on the lower and upper edges of the plate (models :math:`A` :math:`C`, :math:`D`, :math:`E`) or subjected to a volume force and an embedment on the upper part (modeling :math:`B`), or subjected to pressure on the lips (modeling). :math:`F`).

Different models are considered:


1. modeling :math:`A`: :math:`\text{X-FEM}\mathrm{2D}`, edge surface loading, cells QUAD4, geometric enrichment


2. modeling :math:`B`: :math:`\text{X-FEM}\mathrm{2D}`, volume loading, cells QUAD4. geometric enrichment


3. modeling :math:`C`: :math:`\text{X-FEM}\mathrm{2D}`, edge surface loading, grid TRIA3, geometric enrichment


4. modeling :math:`D`: :math:`\text{X-FEM}\mathrm{2D}`, edge surface loading, mesh TRIA3, topological enrichment


5. Modeling :math:`E`: :math:`\text{X-FEM}\mathrm{2D}`, edge surface loading, TRIA6 meshes, topological enrichment


6. modeling :math:`F`: :math:`\text{X-FEM}\mathrm{2D}`, lip loading, mesh TRIA3, topological enrichment

The validation focuses on stress intensity factors (:math:`{K}_{I}` and :math:`{K}_{\mathrm{II}}`), in comparison with the analytical solution for models :math:`A`, :math:`C`, :math:`D`, :math:`E`, :math:`F` and a non-regression solution for modeling :math:`B`.


.. toctree::
    :hidden:

    self

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

    Probl_me_de_r_f_rence
    Mod_lisation_A
    Mod_lisation_B
    Mod_lisation_C
    Mod_lisation_D
    Mod_lisation_E
    Mod_lisation_F
    Synth_ses_des_r_sultats