Modeling A
==============


Characteristics of modeling
-----------------------------------

The modeling of ductile rupture is carried out with modeling AXIS_INTERFACE and law CZM_TRA_MIX. Volume elements are modeled with model AXIS.


Characteristics of the mesh
----------------------------

The input mesh is linear. It is transformed into a quadratic mesh by LINE_QUAD in CREA_MAILLAGE.

After the transformation, its characteristics are as follows:

Number of knots: 962

Count of elements: 280 QUAD8.

Number of interface elements: 15 QUAD8.


Tested sizes and results
------------------------------

**Non-regression test**: diametral contraction (:math:`\mathrm{-}2\mathrm{\times }\mathit{DX}` from point :math:`B`), traction force (the resultant :math:`\mathit{DY}` of REAC_NODA out of :math:`\mathit{CD}` multiplied by :math:`2\pi`) as a function of the tensile displacement :math:`\mathit{DY}` (on :math:`\mathit{CD}`).

For a shift from :math:`\mathrm{0,3}\mathrm{mm}` according to :math:`Y` to :math:`\mathit{CD}`

.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Tolerance (** :math:`\text{\%}` **)**"
    "Contraction (:math:`\mathrm{mm}`)", "0.605676", "0.10"
    "Force (:math:`\mathit{kN}`)", "28.8696", "0.10"


For a shift from :math:`\mathrm{0,4}\mathrm{mm}` according to :math:`Y` to :math:`\mathrm{CD}`

.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Tolerance (** :math:`\text{\%}` **)**"
    "Contraction (:math:`\mathrm{mm}`)", "0.931629", "0.10"
    "Force (:math:`\mathrm{kN}`)", "23.6023", "0.10"


**Non-regression test on the calculation performed with the Rousselier model**: diametral contraction (:math:`\mathrm{-}2\mathrm{\times }\mathit{DX}` from point :math:`B`), traction force (the resultant :math:`\mathit{DY}` of REAC_NODA out of :math:`\mathrm{CD}` multiplied by :math:`2\pi`) as a function of the traction displacement (:math:`\mathit{DY}` on :math:`\mathrm{CD}`).

For a shift from :math:`\mathrm{0,2}\mathit{mm}` according to :math:`Y` to :math:`\mathit{CD}`

.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Rousselier**", "**Error (** :math:`\text{\%}` **)**) **"
    "Contraction (:math:`\mathit{mm}`)", "0.333202", "0.349885", "4.8"
    "Force (:math:`\mathit{kN}`)", "29.3851", "29.3597", "0.087"


For a shift from :math:`\mathrm{0,3}\mathit{mm}` according to :math:`Y` to :math:`\mathit{CD}`

.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Rousselier**", "**Error (** :math:`\text{\%}` **)**) **"
    "Contraction (:math:`\mathit{mm}`)", "0.605676", "0.605676", "0.620591", "2.4"
    "Force (:math:`\mathit{kN}`)", "28.8696", "28.8696", "28.6069", "0.92"


For a shift from :math:`\mathrm{0,4}\mathit{mm}` according to :math:`Y` to :math:`\mathit{CD}`

.. csv-table::

    "**Size tested**", "**Code_Aster**", "**Rousselier**", "**Error (** :math:`\text{\%}` **)**) **"
    "Contraction (:math:`\mathit{mm}`)", "0.931629", "0.931629", "0.954683", "2.4"
    "Force (:math:`\mathit{kN}`)", "23.5744", "22.6731", "22.6731", "04/01/00"