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


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


.. image:: images/1000068E00001B63000017AB3D137CA7BDA6AF2A.svg
    :width: 353
    :height: 305


.. _RefImage_1000068E00001B63000017AB3D137CA7BDA6AF2A.svg:

Loading and boundary conditions are modelled by:

On node N04, DX=DY=0

On node N08, DX=DY=DZ=0

On node N02, DX=0.

On node N06, DX=0.

A nodal force is imposed on:

(N01 N03 N05 N07), :math:`\mathit{FX}=-\text{}\frac{1}{4}{\sigma }_{d}(t)`, :math:`\mathit{FY}=-\text{}\frac{1}{4}{\tau }_{d}(t)`

(N03 N04 N07 N08), :math:`\mathit{FX}=-\text{}\frac{1}{4}{\tau }_{d}(t)`

(N02 N04 N06 N08), :math:`\mathit{FY}=\frac{1}{4}{\tau }_{d}(t)`

(N01 N02 N05 N06), :math:`\mathit{FX}=\frac{1}{4}{\tau }_{d}(t)`

The mechanical calculation is carried out with VonMises's elasto-plastic behavior law with linear isotropic work hardening (key word' RELATION = META_P_IL ') and in large deformations (keyword' DEFORMATION = SIMO_MIEHE ')


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


.. csv-table::

    "Number of knots:", "8"
    "Number of meshes and type:", "1 HEXA8, 4 QUAD4"



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


.. csv-table::

    "**Variables**", "**Moments (** :math:`s` **)**", "**Reference Type**", "**Reference**", "**% tolerance**"
    ":math:`{\sigma }_{\mathit{xx}}` ", "1"," AUTRE_ASTER ", "148.56612701"," :math:`{1.E}^{-8}`"
    ":math:`{\sigma }_{\mathit{xy}}` ", "1"," AUTRE_ASTER ", "94.6669933181"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xx}}` ", "1"," AUTRE_ASTER ", "0.015468475646"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{yy}}` ", "1"," AUTRE_ASTER ", "-0.00768174092805"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xy}}` ", "1"," AUTRE_ASTER ", "0.0141972994127"," :math:`{1.E}^{-8}`"
    ":math:`{\sigma }_{\mathit{xx}}` ", "2"," AUTRE_ASTER ", "248.713357259"," :math:`{1.E}^{-8}`"
    ":math:`{\sigma }_{\mathit{xy}}` ", "2"," AUTRE_ASTER ", "27.5330374296"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xx}}` ", "2"," AUTRE_ASTER ", "0.0385022874704"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{yy}}` ", "2"," AUTRE_ASTER ", "-0.0195587811987"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xy}}` ", "2"," AUTRE_ASTER ", "0.0210883631486"," :math:`{1.E}^{-8}`"
    ":math:`{\sigma }_{\mathit{xx}}` ", "3"," AUTRE_ASTER ", "1.409651686078"," :math:`{1.E}^{-8}`"
    ":math:`{\sigma }_{\mathit{xy}}` ", "3"," AUTRE_ASTER ", "0.718644752334"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xx}}` ", "3"," AUTRE_ASTER ", "0.037173466674"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{yy}}` ", "3"," AUTRE_ASTER ", "-0.0191595912069"," :math:`{1.E}^{-8}`"
    ":math:`{\epsilon }_{\mathit{xy}}` ", "3"," AUTRE_ASTER ", "0.0209115907367"," :math:`{1.E}^{-8}`"