B modeling
==============


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

3D **(** HEXA8 **)**

1 element, stress field and uniform deformation.


.. image:: images/Shape4.gif


.. _RefSchema_Shape4.gif:


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

Number of knots: 8

Number of meshes and type: 1 HEXA8


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

The non-zero components of the stress field SIGM_ELNO (component :math:`\mathrm{xx}`, :math:`\mathrm{zz}` and :math:`\mathrm{xz}`), the cumulative plastic deformation under tension (second internal variable, second component of the field VARI_ELNO), and finally, only for the fourth case of loading (discharge), the cumulative plastic deformation in compression, were tested, and finally, only for the fourth case of loading (discharge), the cumulative plastic deformation in compression, (first internal variable, first component of the field), were tested. VARI_ELNO).

The first three loads correspond to the load, and have reference results. The fourth load corresponds to the discharge, and is a result of non-regression of the code.

**Field** **SIGM_ELNO component** **SIXX**


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For an imposed move under load :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "0.152474", "0.1524472", "0.018"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "8.492877.10—2", "8.487797.10—2", "0.060"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "1.732484.10—2", "1.730871.10—2", "0.434"
    "For a displacement imposed at landfill :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "—4.386134.10—5", "-"


(*) at the landfill, a non-regression test is carried out. There is no calculated analytical solution.

**Field** **SIGM_ELNO component** **SIZZ**


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "0.210300", "0.210265", "0.016"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "0.117138", "0.117069", "0.059"
    "For a displacement imposed by load :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "2.397743.10—2", "2.387336.10—2", "0.434"
    "For a displacement imposed at landfill :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "—4.768217.10—5", "-"


(*) at the landfill, a non-regression test is carried out. There is no calculated analytical solution.

**Field** **SIGM_ELNO component** **SIXZ**


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For an imposed displacement under load :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "—5.007871.10—2", "—5.007226.10—2", "0.013"
    "For an imposed displacement under load :math:`{U}_{1}=0.2` and :math:`{U}_{2}=0.10` ", "—2.789472.10—2", "—2.787871.10—2", "0.057"
    "For an imposed displacement under load :math:`{U}_{1}=0.3` and :math:`{U}_{2}=0.15` ", "—5.709873.10—3", "—5.685155.10—3", "0.433"
    "For a displacement imposed at landfill :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "(*)", "—3.308936.10—6", "-"


(*) at the landfill, a non-regression test is carried out. There is no analytical solution.

**Field** **VARI_ELNO component** **** VARI_2 (cumulative plastic deformation under tension) **


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For an imposed displacement under load :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "1.085728.10—2", "1.085728.10—2", "5.10—9"
    "For an imposed displacement under load :math:`{U}_{1}=0.2` and :math:`{U}_{2}=0.10` ", "2.171556.10—2", "2.171556.10—2", "5.10—9"
    "For an imposed displacement under load :math:`{U}_{1}=0.3` and :math:`{U}_{2}=0.15` ", "3.257385.10—2", "3.257385.10—2", "4.10—9"
    "For a displacement imposed at landfill :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "3.257385.10—2", "3.257385.10—2", "4.10—9"


(*) at the landfill, a non-regression test is carried out. There is no calculated analytical solution.

**Field** **VARI_ELNO component** **** VARI_1 (cumulative plastic deformation under compression) **


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For a displacement imposed at landfill :math:`{U}_{1}=0.1` and :math:`{U}_{2}=0.05` ", "(*)", "3.528401.10—1", "-"


(*) at the landfill, a non-regression test is carried out. There is no calculated analytical solution.