3. Modeling A#
3.1. Characteristics of modeling#
3D modeling is implemented. Isotropic, transverse and orthotropic materials are tested (with possible consideration of thermal deformations).
Notes:
Transverse isotropy is not tested for plane stresses because this case corresponds to isotropy.
For the axisymmetric case, the stress field depends on the calculation point.
This point is chosen at the point of integration of the triangle (i.e. it is the center of gravity of the triangle).
We recall that orthotropy in any coordinate system is not available for Fourier modeling because there is then coupling of all the components of the stress tensor:
The current implementation makes it possible to use only the symmetric components from which the antisymmetric components can be found, but for this to be possible, slips must not induce tensile stresses.
3.2. Characteristics of the mesh#
We have a 4-node tetrahedron element \(\mathrm{ABCD}\).
3.3. Tested values#
Identification |
Reference |
Case of 3D transverse isotropy |
|
result name: \(\mathit{Mest1}\) |
|
displacement field |
|
\(\mathit{dy}(c)\) |
21 |
field EPSI_ELGA |
|
\(\mathit{EPXY}\) |
3 |
\(\mathit{EPXZ}\) |
4 |
\(\mathit{EPYZ}\) |
6 |
field SIEF_ELGA |
|
\(\mathit{SIXX}\) |
43310.760 |
\(\mathit{SIYY}\) |
72798.710 |
\(\mathit{SIZZ}\) |
62459.356 |
\(\mathit{SIXY}\) |
39567.891 |
\(\mathit{SIXZ}\) |
31078.597 |
\(\mathit{SIYZ}\) |
84049.301 |
field SIGM_ELNO |
|
\(\mathit{SIXX}\) |
43310.760 |
Champ emel—elga Ep |
1.19123 E6 |
Champ emel—elno—elga Ep |
1.19123 E6 |
Case of 3D orthotropy |
|
result name: \(\mathit{Mest2}\) |
|
displacement field |
|
\(\mathit{dy}(c)\) |
21 |
field EPSI_ELGA |
|
\(\mathit{EPXY}\) |
3 |
\(\mathit{EPXZ}\) |
4 |
\(\mathit{EPYZ}\) |
6 |
field SIEF_ELGA |
|
\(\mathit{SIXX}\) |
601.8754 |
\(\mathit{SIYY}\) |
80053.665 |
\(\mathit{SIZZ}\) |
78596.607 |
\(\mathit{SIXY}\) |
83948.263 |
\(\mathit{SIXZ}\) |
17339.093 |
\(\mathit{SIYZ}\) |
126571.71 |
champ enel—elga \(\mathit{Ep}\) |
1.55286.106 |
champ enel—elno—elga \(\mathit{Ep}\) |
1.55286.106 |
Case of orthotropy taking into account thermal deformations (command STAT_NON_LINE ) |
|
result name: \(\mathit{Mest3}\) |
|
displacement field |
|
\(\mathit{dy}(c)\) |
21 |
Identification |
Reference |
field EPSI_ELGA |
|
\(\mathit{EPXY}\) |
3 |
\(\mathit{EPXZ}\) |
4 |
\(\mathit{EPYZ}\) |
6 |
field SIEF_ELGA |
|
\(\mathit{SIXX}\) |
1226.2014 |
\(\mathit{SIYY}\) |
78597.064 |
\(\mathit{SIZZ}\) |
76585.792 |
\(\mathit{SIXY}\) |
83710.907 |
\(\mathit{SIXZ}\) |
17255.703 |
\(\mathit{SIYZ}\) |
126657.367 |
Case of orthotropy taking into account thermal deformations (command MECA_STATIQUE ) |
|
result name: \(\mathit{Mest4}\) |
|
displacement field |
|
\(\mathit{dy}(c)\) |
21 |
field EPSI_ELGA |
|
\(\mathit{EPXY}\) |
3 |
\(\mathit{EPXZ}\) |
4 |
\(\mathit{EPYZ}\) |
6 |
field SIEF_ELGA |
|
\(\mathit{SIXX}\) |
1226.2014 |
\(\mathit{SIYY}\) |
78597.064 |
\(\mathit{SIZZ}\) |
76585.792 |
\(\mathit{SIXY}\) |
83710.907 |
\(\mathit{SIXZ}\) |
17255.703 |
\(\mathit{SIYZ}\) |
126657.367 |