.. _V6.04.151:

**v6.04.151** SSNV151 - Traction/Compression with the BETON_DOUBLE_DP law of behavior
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**Summary**

This validation case is intended to verify the behavior model :math:`\mathrm{3D}` BETON_DOUBLE_DP formulated in the context of thermoplasticity, for the description of the non-linear behavior of concrete under tension and compression, taking into account irreversible variations in the thermal and mechanical characteristics of concrete, which are particularly sensitive to high temperature.

The description of cracking is treated in the context of plasticity, using energy equivalence, by identifying the cracking energy density in :math:`I` mode, with the plastic work of an equivalent homogeneous medium, where the plastic deformation is uniformly distributed in an "elementary" zone. This approach maintains the continuity of the formulation of the model, throughout its behavior, and contributes to the avoidance of possible numerical difficulties when the state of the material changes.

The pathological sensitivity of the numerical solution to spatial discretization (mesh), generated by the introduction of a softening behavior of concrete under tension and compression, is partially resolved by introducing a cracking or breaking energy, depending on a characteristic length :math:`{l}_{c}`, linked to the size of the elements.

The resolution of the equations constituting the model is carried out by an implicit diagram.

It is an 8-knot cube subjected to uniaxial compression, in forced displacement, to which is added biaxial traction when significant work hardening under tension has been achieved. This loading leads to the particular case of a state of hydrostatic stress, resolved by projection at the top of the traction cone, when using an equivalent stress/hydrostatic stress diagram. This is a non-regression test case.


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    self

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    :maxdepth: 2
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    Probl_me_de_r_f_rence
    Mod_lisation_A