7. E modeling#
7.1. Characteristics of modeling#
3D modeling
Item MECA_TETRA4.
7.2. Characteristics of the mesh#
Number of knots: 4
Number of meshes and types: 1 TETRA4
7.3. Features tested#
Here we test the ENDO_ORTH_BETON law of behavior in 3 loading cases:
\({U}_{1}\): Single pull
\({U}_{2}\): Compression
\({U}_{3}\) :Biaxial loading (tension in the \(y\) direction, compression in the \(x\) direction, with a fixed stress ratio: \({\sigma }_{\mathit{yy}}\mathrm{=}\mathrm{-}0.2{\sigma }_{\mathit{xx}}\))
This test case makes it possible to verify that the set of parameters chosen by the user respects the following data:
tensile failure stresses,
breaking stresses in compression,
no swelling of the rupture envelope for biaxial tests. This consists in verifying that the maximum tensile stress \({\sigma }_{\mathit{yy}}\) of the biaxial test is less than the breaking stress in simple tension.
7.4. Charging path#
Unlike models A, B, C and D, it is the force, and not the displacement, that is imposed here. The PRED_ELAS load control method is used, because the behavior is softening. The following loads are applied:
\({U}_{1}\): \(\mathrm{FX}\) out of \(\mathrm{F1}\), \(-1/\sqrt{3}\mathrm{FX}\) out of \(\mathrm{F4}\), \(\mathrm{FX}<0\) (Traction)
\({U}_{2}\): \(\mathrm{FX}\) out of \(\mathrm{F1}\), \(-1/\sqrt{3}\mathrm{FX}\) out of \(\mathrm{F4}\), \(\mathrm{FX}>0\) (Compression)
\({U}_{3}\): \(\mathrm{FX}\) on \(\mathrm{F1}\), \(-1/\sqrt{3}\mathrm{FX}\) on \(\mathrm{F4}\), \(\mathrm{FX}>0\) (Compression along the \(x\) axis);
\(\mathrm{FY}\) on \(\mathrm{F2}\), \(-1/\sqrt{3}\mathrm{FY}\) on \(\mathrm{F4}\), with \(\mathit{FY}\mathrm{=}\mathrm{-}\mathrm{0,2}\mathit{FX}\) (Traction along the axis \(y\)).
7.5. Tested values#
Instant |
Result |
Field Name |
Component |
Location |
Aster |
||
42 |
|
|
|
|
3.20684E+00 |
||
76 |
|
|
|
|
-3.18000E+01 |
||
74 |
|
|
|
|
-1.42038E+01 |
For each calculation, we test the maximum value (in absolute value) of the constraint \({\sigma }_{\mathit{xx}}\). The breaking stress in tension (\(\mathrm{U1}\)), in compression (\(\mathrm{U2}\)) is then obtained, and it is verified that the tensile stress in the biaxial test (\(\mathrm{U3}\)) is less than the breaking stress in simple tension (\(\mathit{U1}\)):
\(\mathit{U1}\): \({\sigma }_{\mathit{rupture}}^{\mathit{traction}}\mathrm{=}3.20684\mathit{MPa}\)
\(\mathrm{U2}\): \({\sigma }_{\mathit{rupture}}^{\mathit{compression}}\mathrm{=}\mathrm{-}31.8\mathit{MPa}\)
\(\mathrm{U3}\): \({\sigma }_{\mathit{U3}}^{\mathit{traction}}\mathrm{=}\mathrm{-}0.2{\sigma }_{\mathit{U3}}^{\mathit{compression}}\mathrm{=}0.2\mathrm{\times }14.2038\mathit{Mpa}\) and \({\sigma }_{\mathit{U3}}^{\mathit{traction}}<{\sigma }_{\mathit{rupture}}^{\mathit{traction}}\)
Warning 1: There may not be enough time to reach the softening phase. The user will therefore check that for calculations \(\mathit{U1}\) and \(\mathrm{U2}\), since calculation \(\mathrm{U3}\) is subject to an additional warning (cf. warning 2), it is in the softening phase (reduction of the control parameter). The absolute maximum stress must not be reached for the last step of time. If not, the calculation must continue until the softening phase.
Warning2: It is possible, for certain sets of parameters, to observe convergence difficulties for calculation \(\mathrm{U3}\) during the softening phase. In fact, the law of behavior ensures the existence and the uniqueness of the solution in imposed deformation, but not in imposed force. Since these convergence problems only appear in the softening phase, the user will be able to consider the greatest value of the control parameter reached, equal to the greatest compression stress.
achieved in absolute value, as a reference to calibrate \(\mathrm{K2}\). This is only true if there are convergence problems. If there is no convergence problem for calculation \(\mathrm{U3}\), and the absolute maximum stress is reached for the last time step, the calculation must be continued.