3. Modeling A#
3.1. Characteristics of modeling#
This is a D_ PLAN_HM modeling using quadratic HM- XFEM elements. The bar on which the modeling is performed is divided into 5 QUAD8. The interface is unmeshed and cuts off the central element. So we have 3 HM- XFEM elements and 2 classical HM elements. As indicated in the Figure, the 3 elements XFEM are subdivided into sub-triangles (to perform the Gauss-Legendre integration on either side of the lips of the interface, but these triangular sub-elements are not mesh elements).
Figure 3.1-a : Characteristics of modelling
3.2. Characteristics of the mesh#
The mesh consists of 5 quadratic quadratic quadratic cells (QUAD8).
3.3. Tested sizes and results#
The results (resolution with STAT_NON_LINE) are summarized in the table below for the \(y\) direction. To test all the nodes of the bar at the same time, we calculate MIN and MAX.
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DY (below) MIN |
“ANALYTIQUE” |
-4.323558729E-03 |
0.0001 |
DY (below) MAX |
“ANALYTIQUE” |
-4.323558729E-03 |
0.0001 |
DY (above) MIN |
“ANALYTIQUE” |
4.297130927-03 |
0.0001 |
DY (above) MAX |
“ANALYTIQUE” |
4.297130927-03 |
0.0001 |
The results (resolution with STAT_NON_LINE) are summarized in the table below for the \(x\) direction. To test all the nodes of the bar at the same time, we calculate MIN and MAX.
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DX (below) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DX (below) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
DX (above) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DX (above) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
We can then observe (from the Figure) a clear discontinuity in the field of movements linked to the presence of the interface crossing the massif. This suggests that enrichment has been taken into account in the approximation of the displacement field by the Heaviside function.
Figure 3.3-a : Field of movement by direction (Oy)
A second modeling is then carried out which uses the same parameters as the previous one, but this time by performing the calculation XFEM (which is then a pure mechanics calculation) with the operator MECA_STATIQUE instead of the operator STAT_NON_LINE in the case HM-XFEM. The results obtained are strictly identical to the previous ones.