Modeling A ============== Characteristics of modeling ----------------------------------- This is a modeling XFEM, in plane constraints, the discontinuity interface being defined by a level function (level set noted :math:`\text{LN}` for the normal level set) directly in the command file using the DEFI_FISS_XFEM [:ref:`U4.82.08 `] operator. The level function equation for the interface is as follows: :math:`\text{LN}=Y-2.5` No tangential level set is necessary since the keyword TYPE_DISCONTINUITE =' INTERFACE 'is used, which allows the structure to be completely divided into two parts. The cohesive law is introduced through the operator DEFI_CONT, by specifying ALGO_CONT =' CZM ', and the cohesive behavior law is activated using the keyword RELATION =' CZM_EXP_REG'. Here we are testing the :math:`I` and :math:`\mathrm{II}` opening modes. Characteristics of the mesh ---------------------------- We discretize the structure in :math:`1\times 5` finite elements QUAD4. The interface is therefore present in the central element through level sets. .. image:: images/100000000000020D000003345EB71E32E5F2A7C5.png :width: 2.189in :height: 3.4173in .. _RefImage_100000000000020D000003345EB71E32E5F2A7C5.png: **Figure** 3.2-a **: Model A mesh** Piloting -------- A specific control :math:`X-\mathrm{FEM}` SAUT_IMPO is used on all the edges intersected by the crack. Tested sizes and results ------------------------------ *Fashion* :math:`I` *:* The values of contact Lagrangians LAGS_C are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum number of contact Lagrangians. .. csv-table:: "**No**", "**Identification**", "**Reference**", "**Tolerance (%)**" "0.5", "H1Y for all nodes", "1.36362396705485E-07", "1.0E-6" "0.51.0E-6"," LAGS_Cpour all nodes", "3.66296853301E+05", "1.0E-6" "0.75", "H1Y for all nodes", "6.818119835274E-08", "1.0E-6" "0.75"," LAGS_Cpour all nodes", "1.8314842665E+05", "1.0E-6" "2", "H1Y for all nodes", "4.0908719011645E-07", "1.0E-6" "2"," LAGS_Cpour all nodes", "1.098890559903E+06", "1.0E-6" "3.5", "H1Y for all nodes", "7.49999999999582E-04", "1.0E-6" "3,5"," LAGS_Cpour all nodes", "1.75867720687844E+05", "1.0E-6" "4.5", "H1Y for all nodes", "2.49999999999582E-04", "1.0E-6" "4.5"," LAGS_Cpour all nodes", "58622.573562549", "1.0E-6" "5.5", "H1Y for all nodes", "7.49999999999582E-04", "1.0E-6" "5,5"," LAGS_Cpour all nodes", "1.75867720687844E+05", "1.0E-6" "7", "H1Y for all nodes", "1.49999999999958E-03", "1.0E-6" "7"," LAGS_Cpour all nodes", "28117.686527187", "1.0E-6" "9.5", "H1Y for all nodes", "2.49999999999582E-04", "1.0E-6" "9.5"," LAGS_Cpour all nodes", "4686.28108785798", "1.0E-6" "12", "H1Y for all nodes", "1.49999999999958E-03", "1.0E-6" "12"," LAGS_Cpour all nodes", "28117.686527187", "1.0E-6" "15", "H1Y for all nodes", "2.99999999999958E-03", "1.0E-6" "15"," LAGS_Cpour all nodes", "718.731177854856", "1.0E-6" *Fashion* :math:`\mathrm{II}` *:* The values of the Lagrangian friction values LAGS_F1 are tested at all the nodes of the mesh crossed by the interface after convergence of the iterations of each STAT_NON_LINE operator, these values being uniform on the interface. To test all the values at once, we test the minimum and the maximum of the Lagrangian friction values. .. csv-table:: "**No**", "**Identification**", "**Reference**", "**Tolerance (%)**" "0.5", "H1X for all nodes", "1.36362396705485E-07", "1.0E-6" "0.5"," LAGS_F1pour all nodes", "3.66296853301E+05", "1.0E-6" "0.75", "H1X for all nodes", "6.818119835274E-08", "1.0E-6" "0.75"," LAGS_F1pour all nodes", "1.8314842665E+05", "1.0E-6" "2", "H1X for all nodes", "4.0908719011645E-07", "1.0E-6" "2"," LAGS_F1pour all nodes", "1.098890559903E+06", "1.0E-6" "3.5", "H1X for all nodes", "7.49999999999582E-04", "1.0E-6" "3,5"," LAGS_F1pour all nodes", "1.75867720687844E+05", "1.0E-6" "4.5", "H1X for all nodes", "2.49999999999582E-04", "1.0E-6" "4.5"," LAGS_F1pour all nodes", "58622.573562549", "1.0E-6" "5.5", "H1X for all nodes", "7.49999999999582E-04", "1.0E-6" "5,5"," LAGS_F1pour all nodes", "1.75867720687844E+05", "1.0E-6" "7", "H1X for all nodes", "1.49999999999958E-03", "1.0E-6" "7"," LAGS_F1pour all nodes", "28117.686527187", "1.0E-6" "9.5", "H1X for all nodes", "2.49999999999582E-04", "1.0E-6" "9.5"," LAGS_F1pour all nodes", "4686.28108785798", "1.0E-6" "12", "H1X for all nodes", "1.49999999999958E-03", "1.0E-6" "12"," LAGS_F1pour all nodes", "28117.686527187", "1.0E-6" "15", "H1X for all nodes", "2.99999999999958E-03", "1.0E-6" "15"," LAGS_F1pour all nodes", "718.731177854856", "1.0E-6" Comments ------------ The contact and friction values of the Lagrangians are calculated explicitly as a function of the displacement jump that is controlled. It is therefore natural to have almost zero errors.