4. Modeling A#
4.1. Characteristics of modeling#
The cell is homogenized in MASSIF in order to obtain the parameters for a 3D model.
4.2. Tested values#
The values of the homogenized coefficients (elastic and thermal) obtained by the calculation are compared to those of the note [VOLDOIRE93].
Homogenized coefficients |
[] |
Calculation ASTER |
Relative error (%) :math: frac {left|text {approximate value} -text {theoretical value}right|} {left|text {theoretical value}right|}ast 100 |
\({A}_{\text{1111}}\) |
0.48437 |
0.484961 |
0.12% |
\({A}_{\text{2222}}\) |
– |
0.484782 |
– |
\({A}_{\text{3333}}\) |
0.73037 |
0.730671 |
0.04% |
\({A}_{\text{1122}}\) |
0.12246 |
0.122638 |
0.14% |
\({A}_{\text{1133}}\) |
0.18205 |
0.182280 |
0.13% |
\({A}_{\text{2233}}\) |
– |
0.182226 |
– |
\({A}_{\text{1212}}\) |
0.16161 |
0.163213 |
0.98% |
\({A}_{\text{2323}}\) |
– |
0.344923 |
– |
\({A}_{\text{3131}}\) |
0.344589 |
0.344814 |
0.06% |
\({K}_{\text{11}}\) |
0.447967 |
0.448258 |
0.06% |
\({K}_{\text{22}}\) |
– |
0.448399 |
– |
\({K}_{\text{33}}\) |
0.62115 |
0.621319 |
0.03% |
The equalities between the homogenized coefficients described in the preceding paragraph are also verified.
Relationship between homogenized coefficients |
Relative error (%) |
\(\begin{array}{c}{A}_{\text{1111}}^{\text{hom}}-{A}_{\text{2222}}^{\text{hom}}=0\end{array}\) |
0.04% |
\(\begin{array}{c}{A}_{\text{1133}}^{\text{hom}}-{A}_{\text{2233}}^{\text{hom}}=0\end{array}\) |
0.03% |
\(\begin{array}{c}{A}_{\text{3131}}^{\text{hom}}-{A}_{\text{2323}}^{\text{hom}}=0\end{array}\) |
0.03% |
|
0.34% |
\({A}_{\text{1133}}^{\text{hom}}-\nu \text{.}\left({A}_{\text{1111}}^{\text{hom}}+{A}_{\text{1122}}^{\text{hom}}\right)=0\) |
1.6e -04% |
\({A}_{\text{3}\mathrm{\alpha }\text{3}\mathrm{\alpha }}^{\text{hom}}-\frac{2\mathrm{\mu }}{k}{K}_{\text{11}}^{\text{hom}}=0\) |
2.7th -05% |