3. Modeling B: Horizontal interfaces in closure

3.1. Characteristics of the mesh and the interface

The mesh is the same as that of modeling A. The objective being to test contact management on the interfaces represented with X- FEM, only the boundary conditions have changed.

3.2. Boundary conditions

This time, the boundary conditions will make it possible to test the consideration of contact without friction on the lips of the interfaces. We therefore maintain the embedment of the nodes belonging to the median surface but the displacements imposed on the nodes at the two extremes (lower and upper) will close the interfaces. So we will have:

GROUP_NO = SURFMED: DX = 0, DY = 0, and DZ = 0

GROUP_NO = SURFINF: DX = 0, DY = 0, and DZ = DEPZ

GROUP_NO = SURFSUP: DX = 0, DY = 0, and DZ = - DEPZ

3.3. Analytical resolution

Since the interfaces are horizontal and the compression state is uniaxial and normal at the interface, there is no possible sliding. The value of the contact pressure is checked and the solution of the problem is that of the same problem without an interface, for each of the blocks on one side and the other of the embedded surface. As shown for test case SSNV182 [V6.04.182] and taking into account the geometry and boundary conditions described in §2.2, the contact pressure is given by:

\(\lambda \mathrm{=}E\frac{\text{DEPZ}}{\text{LZ}\mathrm{/}2}\) eq 4.3-1

With the numeric values previously introduced, \(\lambda \mathrm{=}\mathrm{-}\text{12}{.10}^{3}\text{Pa}\).

3.4. Tested sizes and results

The smooth running of the calculation allows a priori to validate the good management of the contact for multi-cracking. The components of SD FISS_XFEM concerning the contact for each crack are managed correctly at the level of operators MODI_MODELE_XFEM and STAT_NON_LINE. The contact pressure values for the nodes in the middle belonging to the elements cut by the cracks are tested.

Identification	Reference
LAGS_Cpour all the nodes of the two cracks	-1.2E4
LAGS_F1pour all the nodes in the two cracks	0.00
LAGS_F2pour all the nodes in the two cracks	0.00