3. Principle of the test#

The test consists in defining two materials \(\mathit{MAT1}\) and \(\mathit{MAT2}\):

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

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

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

The test then takes place as follows:

  1. material definition \(\mathit{MAT1}\);

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

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

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

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

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

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