Principle of the test
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The test consists in defining two materials :math:`\mathit{MAT1}` and :math:`\mathit{MAT2}`:


* for :math:`\mathit{MAT1}`, constant cohesive parameters are defined via DEFI_MATERIAU/RUPT_FRAG: :math:`\text{GC}={G}_{c}` and :math:`\text{SIGM\_C}={G}_{c}`;


* for :math:`\mathit{MAT2}`, we define via DEFI_MATERIAU/RUPT_FRAG_FOdes cohesive parameters which are functions of triaxiality (noted :math:`\alpha`): :math:`\text{GC}=f(\alpha )\mathrm{.}{G}_{c}` and :math:`\text{SIGM\_C}=f(\alpha )\mathrm{.}{G}_{c}`;

In uniaxial traction, triaxiality is equal to :math:`\alpha =1/3`, we then choose to define for :math:`\mathit{MAT2}` a linear dependence on triaxiality with a slope equal to :math:`3`: :math:`f(\alpha )=3\alpha`. In this way: the values of the parameters of the cohesive law in :math:`\mathit{MAT2}` must remain constant and the same as those chosen in :math:`\mathit{MAT1}` throughout the loading history.

The test then takes place as follows:


1. material definition :math:`\mathit{MAT1}`;


2. first call to STAT_NON_LINE with :math:`\mathit{MAT1}` up to an imposed travel level below :math:`{U}_{\mathit{test}}`;


3. call to POST_CZM_FISS on the mechanical result previously obtained;


4. definition of material :math:`\mathit{MAT2}` using the triaxiality map obtained with POST_CZM_FISS as the control variable;


5. with material :math:`\mathit{MAT1}`, continuation of the calculation with STAT_NON_LINE from the mechanical state obtained at point 2 until loading :math:`{U}_{\mathit{test}}`;


6. with material :math:`\mathit{MAT2}`, continuation of the calculation with STAT_NON_LINE from the mechanical state obtained at point 2 until loading :math:`{U}_{\mathit{test}}`.

It is then ensured that the results obtained under load :math:`{U}_{\mathit{test}}` in steps 5 and 6 are in agreement with the analytical solution presented above.