14. L modeling#
14.1. Characteristics of modeling#
This is a modeling \(X-\mathrm{FEM}\), in plane constraints, with the definition of contact on the discontinuity interface defined by a level function (level set noted \(\text{LN}\) for the normal level set) directly in the command file using the operator DEFI_FISS_XFEM [U4.82.08].
The slave/master status for a contact surface \(X-\mathrm{FEM}\) is given by the sign of the normal level function \(\text{LN}\): the slave surface is on the negative side while the master surface is located on the positive side.
The level function equation for the interface is as follows:
\(\text{LN}=Y-2.5\)
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.
This test models an opening and closing interface for which the movement jump is controlled by SAUT_IMPO control.
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”. In closure, contact is managed by a term of penalization included in the cohesive law.
14.2. Characteristics of the mesh#
The mesh is the same as in modeling \(A\). The interface is therefore present in the central element through level sets.
14.3. Boundary conditions#
The boundary conditions are the same as those in mode \(I\) for opening \(\mathrm{2D}\) models. The values of COEF_MULT are modified to take a time step when opening and then a time step when closing.
Final calculation instant |
Phase |
Final move jump (in \(m\) ) |
\({c}_{\mathrm{mult}}\) |
|
0.5 |
Traction |
2.73E-7 |
3.6667E6 |
1.36362396705485485E-07 |
1.0 |
Compression |
-2,73E-7 |
-9.16675E5 |
-1.36362396705485485E-07 |
14.4. Reference solution#
First, the solution is given by the cohesive law in paragraph 2.
In closure, the penalized solution is equal to the product of the displacement jump by the penalty coefficient, which is the same as the adhesion coefficient given that we entered PENA_CONTACT =1. (see documentation [R7.02.11]).
14.5. Tested sizes and results#
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. To test all the values at once, we test the minimum and the maximum number of contact Lagrangians.
No |
Identification |
Reference |
Tolerance (%) |
0.5 |
H1Y for all nodes |
1.36362396705485E-07 |
1.0E-10 |
0.5 |
|
3.66296853301E+05 |
1.0E-10 |
1 |
H1Y for all nodes |
-1.36362396705485E-07 |
1.0E-10 |
1 |
|
-3.66296853301E+05 |
1.0E-10 |
14.6. Comments#
This test shows that the term penalization included in the law of cohesive behavior for the treatment of contact makes it possible to eliminate the incompatibility between contact in a continuous method and control. It remains up to the user to verify that the interpenetration obtained remains physical, and increase PENA_CONTACT if this is not the case.
The values of the contact Lagrangians are calculated explicitly as a function of the displacement jump that is controlled. It is therefore natural to have almost zero errors.