.. _V6.04.182:

**v6.04.182** SSNV182 — Block with interface in friction contact with X- FEM
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**Summary**

The purpose of this test is to validate the consideration of contact on the lips of the crack, by limiting itself to the case where the crack completely crosses the structure. Contact is taken into account by the continuous method [:ref:`bib1 <bib1>`] adapted to the framework of the X- FEM method [:ref:`bib2 <bib2>`]. Two contact algorithms are tested: the augmented Lagrangian method and the penalized method [:ref:`bib2 <bib2>`].

This test involves a parallelepipedic block in compression modelled in :math:`\mathrm{2D}` and :math:`\mathrm{3D}`. The interface crossing it is represented by a level-set as part of the X- FEM method. Several angular positions of the interface are taken into account: the interface follows the faces of the elements (:math:`\theta =0°`) and the interface cuts the elements (:math:`\theta =26.56°` in :math:`\mathrm{3D}` and :math:`\theta =30°` in :math:`\mathrm{2D}`). By taking a Coulomb coefficient of friction high enough for there to be adhesion, we find the solution of the same problem without an interface. The d, e and f models make it possible to validate the method also in :math:`\mathrm{2D}`.


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

    Probl_me_de_r_f_rence
    Mod_lisation_A___interface_droite__m_thode_du_Lagrangien_augment_
    Mod_lisation_B___interface_pench_e__m_thode_du_Lagrangien_augment_
    Mod_lisation_C___interface_droite_et_sous-int_gration__m_thode_du_Lagrangien_augment_
    Mod_lisation_D___interface_droite_en_contraintes_planes__m_thode_du_Lagrangien_augment_
    Mod_lisation_E___interface_pench_e_en_contraintes_planes__m_thode_du_Lagrangien_augment_
    Mod_lisation_F___interface_pench_e_en_d_formations_planes__m_thode_du_Lagrangien_augment_
    Mod_lisation_G___interface_droite__m_thode_p_nalis_e
    Mod_lisation_H___interface_pench_e__m_thode_p_nalis_e
    Mod_lisation_I___interface_droite_en_contraintes_planes__m_thode_p_nalis_e
    Mod_lisation_J___interface_pench_e_en_contraintes_planes__m_thode_p_nalis_e
    Mod_lisation_K___interface_droite_en_contraintes_planes__m_thode_du_Lagrangien_augment__sur_un_maillage_quadratique
    Mod_lisation_L___interface_pench_e_en_contraintes_planes__m_thode_du_Lagrangien_augment__sur_un_maillage_quadratique
    Mod_lisation_M___interface_pench_e_en_3D__m_thode_du_Lagrangien_augment__sur_un_maillage_quadratique
    Synth_ses_des_r_sultats