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

The purpose of this test is to validate the damage part of behavior model BETON_RAG.


Geometry
---------

The test is based on a unit cubic finite element (1 m x 1 m).


Property of the law of behavior
-----------------------------------

Young's module: :math:`E=32000\mathrm{MPa}`

Poisson's ratio: :math:`\mathrm{\nu }=0.2`

Parameter of fragility of concrete under tension: :math:`\mathit{MT}=\mathrm{1,7}`

Parameter of fragility of concrete under compression: :math:`\mathit{MC}=\mathrm{1,5}`

Equivalent tensile stress of concrete: :math:`{\mathrm{\sigma }}_{\mathit{ft}}=5.66\mathit{MPa}`

Equivalent stress of concrete in compression: :math:`{\mathrm{\sigma }}_{\mathit{fc}}=38.3\mathit{MPa}`

Angle of the Drucker Prager criterion: :math:`\mathrm{\alpha }=\mathrm{0,15}\mathit{rad}`


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

The loading, applied to the nodes of the X=1m plane, consists in the application of two load cycles in tension and then of two load cycles in compression:


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|Control while moving                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |                                                                                                                            |
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| 1.pull :math:`{\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{1,4}{.10}^{\mathrm{-}4}` 2.release to :math:`{\sigma }_{\mathit{xx}}\mathrm{=}0` 3.pull :math:`{\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{1,0}{.10}^{\mathrm{-}3}` 4.compression :math:`{\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{-}\mathrm{4,0}{.10}^{\mathrm{-}3}` 5.release to :math:`{\sigma }_{\mathit{xx}}\mathrm{=}0` 6.compression :math:`{\epsilon }_{\mathit{xx}}\mathrm{=}\mathrm{-}\mathrm{5,0}{.10}^{\mathrm{-}3}` 7.pull 7.pull :math:`{\epsilon }_{\mathit{xx}}\mathrm{=}0`                                   |    :width: 3.5429in                                                                                                        |
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The following boundary conditions apply:

- for the nodes in the plane X=0 → DX = 0

- for node N1 (0, 0, 0) → DX = DY = DZ = 0

- for node N5 (0, 0, 1) → DY = 0


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