3. Modeling A#
3.1. Characteristics of modeling#
Modeling: C_ PLAN.
The structure is a healthy rectangle, in which an interface is introduced directly into the command file using the DEFI_FISS_XFEM [U4.82.08] operator. The interface is present at a distance \({L}_{Y}\mathrm{=}\mathrm{1,8}m\) from the top edge of the plate.
3.2. Characteristics of the mesh#
Number of knots: 661
Number of meshes and types: 200 QUAD8 for the plate and 50 SEG3 for the edges.

Figure 3.2‑a: 2D quadrangle mesh and interface position
3.3. Tested sizes and results#
The movements resulting from the operator STAT_NON_LINE are post-processed in order to recover the values at the nodes of the crack from the new mesh.
Identification |
Reference |
Aster |
tolerance |
\(\mathrm{DX}\) at point \(A\) |
1.10-5 |
Analytical |
1.10-12 |
\(\mathrm{DX}\) at point \(B\) |
-1.10-5 |
Analytical |
1.10-12 |
\(\mathrm{DY}\) at point \(A\) |
5,52.10-6 |
Analytical |
1.10-12 |
\(\mathrm{DY}\) at point \(B\) |
5,52.10-6 |
Analytical |
1.10-12 |
\(\mathrm{DY}\) at point \(O\) |
8,02.10-6 |
Analytical |
1.10-12 |
3.4. Comments#
This test validates:
the calculation of the stiffness matrix and the second member vectors (taking into account the pressure distributed over elements with quadratic edges),
X- FEM post-processing of \(\mathrm{P2}\) elements.