Reference problem
=====================

Geometry
---------

Consider a reinforced concrete cube with side :math:`L\mathrm{=}1m`.


.. image:: images/10000200000001CC0000015FEE937DCCD077ECF4.png
    :width: 2.9516in
    :height: 2.5457in


.. _RefImage_10000200000001CC0000015FEE937DCCD077ECF4.png:

The reinforcement sheets belong to the plane defined by the four :math:`\mathit{N05}\mathrm{-}\mathit{N02}\mathrm{-}\mathit{N03}\mathrm{-}\mathit{N08}` nodes.

Two reinforcement layers are defined: one in the local direction :math:`X` and one in the local direction :math:`Y`.

The reinforcement rate for each reinforcing sheet is :math:`0.1{m}^{2}\mathrm{/}\mathit{ml}` (Section per linear meter).


Characteristics of the models
----------------------------------

The concrete mesh is modelled with a hexa8 element.

The models considered for reinforcing plies are:

• modeling A (§3): use of grid_membranewith tria3 support meshes

• modeling B (§4): use of grid_membrane with quad4 support meshes

• C modeling (§5): use of grille_excenter with tria3 support meshes


Material properties
------------------------

The concrete material is isotropic elastic whose properties are:

• :math:`{E}_{b}=20000\mathrm{MPa}`

• :math:`\nu =0.2`

The law of behavior of reinforcements follows an elastoplastic model whose properties are:

• :math:`{E}_{a}=200000\mathrm{MPa}`

• :math:`\nu =0`

• :math:`{E}_{\mathrm{ecr}}^{\mathrm{acier}}=20000\mathrm{MPa}`

• :math:`{\sigma }_{e}^{\mathrm{acier}}=200000\mathrm{MPa}`

The grid_isot_line model for isotropic work hardening plasticity is used in stat_non_line.


Boundary conditions and loads
-------------------------------------


.. image:: images/10000200000001A5000001425BD1DA55CB9AE19C.png
    :width: 3.1063in
    :height: 2.5563in


.. _RefImage_10000200000001A5000001425BD1DA55CB9AE19C.png:

Boundary conditions:

• Embedding in :math:`\mathit{A1}`

• :math:`\mathit{DX}\mathrm{=}0` on the :math:`\mathit{A1}\mathrm{-}\mathit{A4}` ridge

• :math:`\mathit{DY}\mathrm{=}0` on the :math:`\mathit{A1}\mathrm{-}\mathit{A2}` ridge

• :math:`\mathrm{DZ}=0` on the bottom surface of the cube (N01-N02-N03-N04)

Charging by mandatory trips:

• :math:`\mathrm{DX}=1` on the :math:`\mathit{A2}\mathrm{-}\mathit{A3}` ridge

• :math:`\mathit{DY}\mathrm{=}1t` on the :math:`\mathit{A3}\mathrm{-}\mathit{A4}` ridge

where :math:`t` is the pseudotime parameter.


Initial conditions
--------------------

Initially, travel and constraints were zero everywhere.