H modeling
==============


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

Plane stress modeling with sub-integration: C_ PLAN_SI

Loading and boundary conditions are modelled by:



.. image:: images/100000000000013200000111F70B98F1C49A635E.png
    :width: 1.7102in
    :height: 1.4929in


.. _RefImage_100000000000013200000111F70B98F1C49A635E.png:


* Dirichlet condition (keyword DDL_IMPO):


* Node :math:`\mathrm{N04}`, :math:`x=y=0`,


* Knots :math:`\mathrm{N02}`, :math:`\mathit{NS2}` :math:`x=0`.


* Neumann condition, surface forces (keyword FORCE_CONTOUR):


* on the faces (skin elements): (1, 2), (2, 4), (4, 3) and (3, 1).


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

Number of knots: 8

Number of meshes and types: 1 QUAD8, 4 SEG3


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


Case of VMIS_ISOT_LINE
~~~~~~~~~~~~~~~~~~~~~~~


.. csv-table::

    "**Identification**", "**Reference type**", "**Reference value**", "**Tolerance**"
    ":math:`{\sigma }_{\mathrm{xx}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1,512E+002"," 0.1%"
    ":math:`{\sigma }_{\mathrm{xy}}` at the moment :math:`A` ", "'ANALYTIQUE'", "9,310E+001"," 0.1%"
    ":math:`p` at the moment :math:`A` ", "'ANALYTIQUE'", "2.0547E-002"," 0.1%"
    "Triaxiality rate :math:`\mathit{TRIAX}` at time :math:`A` ", "'ANALYTIQUE'", "2.2800E-001"," 0.1%"
    ":math:`{\varepsilon }_{\mathrm{xx}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1.48297E-002"," 0.1%"
    ":math:`{\varepsilon }_{\mathrm{xy}}` at the moment :math:`A` ", "'ANALYTIQUE'", "1.36014E-002"," 0.1%"
    "Plastic indicator :math:`\mathit{V2}` at the moment :math:`A` ", "'ANALYTIQUE'", "1.0"," 0.1%"
    ":math:`p` at the moment :math:`B` ", "'ANALYTIQUE'", "4,23293E-002"," 1.0%"
    "Triaxiality rate :math:`\mathit{TRIAX}` at time :math:`B` ", "'ANALYTIQUE'", "3.25349E-001"," 0.1%"
    ":math:`{\varepsilon }_{\mathit{xx}}` at the moment :math:`B` ", "'ANALYTIQUE'", "3,5265E-002"," 1,0%"
    ":math:`{\mathrm{\epsilon }}_{\mathit{xy}}` at the moment :math:`B` ", "'ANALYTIQUE'", "2,0471E-002"," 1.0%"
    ":math:`{\mathrm{\epsilon }}_{\mathit{xx}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "3,3946E-002"," 1.0%"
    ":math:`{\mathrm{\epsilon }}_{\mathit{xy}}^{p}` at the moment :math:`B` ", "'ANALYTIQUE'", "2,0250E-002"," 1.0%"


as well as the charge-discharge indicators:


.. csv-table::

    "**Identification**", "**Reference Type**", "**Value**", "**Tolerance**"
    "INDIC_ENER at the moment :math:`A` ", "'ANALYTIQUE'", "0"," 0.1%"
    "INDIC_ENER at the moment :math:`B` ", "'ANALYTIQUE'", "3,26E-002"," 3,0%"
    "INDIC_SEUIL at the moment :math:`A` ", "'ANALYTIQUE'", "0"," 0.1%"
    "INDIC_SEUIL at the moment :math:`B` ", "'ANALYTIQUE'", "3,26E-002"," 3,0%"
    "INDIC_ENER at the moment :math:`C` (full discharge)", "'ANALYTIQUE'", "4,69E-002"," 3,0%"
    "INDIC_SEUIL at the moment :math:`B` ", "'ANALYTIQUE'", "9.71E-002"," 1.0%"
    "INDIC_SEUIL at time :math:`C` (full discharge)", "'ANALYTIQUE'", "1.0"," 1.0%"
    "DERA_ELNO/RADI_Và the moment 0.1", "'ANALYTIQUE'", "0.0"," 1.0%"



Case of VMIS_ECMI_LINE
~~~~~~~~~~~~~~~~~~~~~~~

We calculate the energies during resolution and compare with case VMIS_ISOT_LINE:


.. csv-table::

    "**Identification**", "**Reference Type**", "**Value**", "**Tolerance**"
    "ETOT_ELGA/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ETOT_ELGA/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ETOT_ELGA/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ETOT_ELGA/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"
    "ETOT_ELNO/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ETOT_ELNO/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ETOT_ELNO/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ETOT_ELNO/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"
    "ETOT_ELEM/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ETOT_ELEM/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ETOT_ELEM/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ETOT_ELEM/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"


We recalculate the energies by POST_ELEM and compare with the case VMIS_ISOT_LINE:


.. csv-table::

    "**Identification**", "**Reference Type**", "**Value**", "**Tolerance**"
    "ENER_TO2/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ENER_TO2/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ENER_TO2/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ENER_TO2/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"
    "ENER_TO3/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ENER_TO3/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ENER_TO3/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ENER_TO3/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"
    "ENER_TO4/TOTALE at the moment 0.1", "'AUTRE_ASTER'", "1.16403E-03"," 0.1%"
    "ENER_TO4/TOTALE at the moment 0.9", "'AUTRE_ASTER'", "1.84340"," 0.1%"
    "ENER_TO4/TOTALE at the moment 2.0", "'AUTRE_ASTER'", "9.58487"," 0.1%"
    "ENER_TO4/TOTALE at the moment 3.0", "'AUTRE_ASTER'", "9.40794"," 0.1%"


The charge-discharge indicators are validated:


.. csv-table::

    "**Identification**", "**Reference Type**", "**Value**", "**Tolerance**"
    "INDIC_ENER at the moment :math:`A` ", "'ANALYTIQUE'", "0"," 0.1%"
    "INDIC_ENER at the moment :math:`B` ", "'ANALYTIQUE'", "3,26E-002"," 3,0%"
    "INDIC_SEUIL at the moment :math:`A` ", "'ANALYTIQUE'", "0"," 0.1%"
    "INDIC_ENER at the moment :math:`C` (full discharge)", "'ANALYTIQUE'", "4,69E-002"," 3,0%"
    "INDIC_SEUIL at the moment :math:`B` ", "'ANALYTIQUE'", "9.71E-002"," 1.0%"
    "INDIC_SEUIL at time :math:`C` (full discharge)", "'ANALYTIQUE'", "1.0"," 1.0%"
    "DERA_ELNO/RADI_Và the moment 0.1", "'ANALYTIQUE'", "0.0"," 1.0%"