5. C modeling#
5.1. Characteristics of modeling#
This is a 3D_HM modeling using quadratic HM- XFEM elements. The column on which the modeling is performed is divided into 5 HEXA20. The interface is unmeshed and cuts off the central element. So we have 3 HM- XFEM elements and 2 classical HM elements (the two hexahedra that form the ends of the column). As indicated in the Figure, the 3 elements XFEM are subdivided into sub-tetrahedra (to perform the Gauss-Legendre integration on either side of the lips of the interface, but these tetrahedral sub-elements are not elements of the mesh).
Figure 5.1-a : Characteristics of modelling
5.2. Characteristics of the mesh#
The mesh consists of 5 quadratic hexahedral cells (HEXA20).
5.3. Tested sizes and results#
The results (resolution with STAT_NON_LINE) are summarised in the tables below. To test all the nodes in the column at the same time, we calculate MIN and MAX.
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DZ (below) MIN |
“ANALYTIQUE” |
-4.323558729E-03 |
0.0001 |
DZ (below) MAX |
“ANALYTIQUE” |
-4.323558729E-03 |
0.0001 |
DZ (above) MIN |
“ANALYTIQUE” |
4.297130927-03 |
0.0001 |
DZ (above) MAX |
“ANALYTIQUE” |
4.297130927-03 |
0.0001 |
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 |
Quantities tested |
Reference type |
Reference value |
Tolerance (%) |
DY (below) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DY (below) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
DY (above) MIN |
“ANALYTIQUE” |
0 |
0.0001 |
DY (above) MAX |
“ANALYTIQUE” |
0 |
0.0001 |
Figure 5.3-a : Field of movement by direction (Oz)
A second modeling is then carried out which uses the same parameters as the previous one, but this time by conducting the calculation XFEM (which is then a pure mechanical 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.