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


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

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

1 element, stress field and uniform deformation.


.. image:: images/Shape3.gif


.. _RefSchema_Shape3.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}` and :math:`\mathrm{zz}`), the component :math:`\mathrm{yy}` of the deformation field EPSI_ELNO, which constitutes an unknown of the system (the deformations in the other two directions being imposed), the cumulative plastic deformation under tension (second internal variable, second component of the field VARI_ELNO) were tested, and finally, only for the fourth case of loading (discharge), the cumulative plastic deformation in compression, (first internal variable, first component of field 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 displacement under load :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "0.1235611", "0.1235380", "0.019"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "6.882374.10—2", "6.878218.10—2", "0.060"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "1.408764.10—2", "1.402639.10—2", "0.435"
    "For a displacement imposed at landfill :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "—4.195092.10—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` ", "0.239212", "0.239174", "0.016"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "0.133243", "0.133165", "0.059"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "2.727403.10—2", "2.725569.10—2", "0.434"
    "For a displacement imposed at landfill :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "—4.959258.10—5", "-"


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

**Field** **EPSI_ELNO component** **EPYY**


.. 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` ", "—3.419463.10—3", "—3.419464.10—3", "2.10—7"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "—6.835813.10—3", "—6.835815.10—3", "2.10—7"
    "For an imposed displacement under load :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "—1.025216.10—2", "—1.025216.10—2", "2.10—7"
    "For a displacement imposed at landfill :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "—4.357498.10—1", "-"


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

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


.. csv-table::

    "**Identification**", "**Reference**", "**Aster**", "**% difference**"
    "For an imposed displacement :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "1.085728.10—2", "1.085728.10—2", "5.10—9"
    "For an imposed displacement :math:`{U}_{1}\mathrm{=}0.2` and :math:`{U}_{2}\mathrm{=}0.10` ", "2.171556.10—2", "2.171556.10—2", "5.10—9"
    "For an imposed displacement :math:`{U}_{1}\mathrm{=}0.3` and :math:`{U}_{2}\mathrm{=}0.15` ", "3.257385.10—2", "3.257385.10—2", "4.10—9"
    "For an imposed displacement :math:`{U}_{1}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}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}\mathrm{=}0.1` and :math:`{U}_{2}\mathrm{=}0.05` ", "(*)", "3.528401.10—1", "-"


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