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SGRC2
Plane or axisymmetric state
Description
Mechanical-flow analysis, Grenoble 2nd gradient method, in large deformations.
The element is defined by 9 nodes specified in NODES in the order indicated in the figure.
Nodes 1, 3, 5, and 7 have 6 DoF ($u_1$, $u_2$, $v_{11}$, $v_{12}$, $v_{21}$, $v_{22}$), whereas nodes 2, 4, 6, and 8 only have 2 DoF ($u_1$, $u_2$). The central node 9 has 4 DoF ($\lambda_{11}$, $\lambda_{12}$, $\lambda_{21}$, $\lambda_{22}$), that have a different signification from ($v_{11}$, $v_{12}$, $v_{21}$, $v_{22}$) but occupy the same position.
The flow description can be completely different from the mechanical description: the pressure can be interpolated linearly in a 4 node configuration, while the mechanical degrees of freedom are interpolated parabolically in an 8-node configuration. In that case, the flow DoF must be fixed for the nodes that are not used (2, 4, 6, and 8).
Type: 218
Implemented by: J-P. Radu, F. Collin (2003)
The framework definition of this element can be found in Pardoen (2015)1).
Files
Prepro: SGRC2A.F
Lagamine: SGRC2B.F
Input file
| Title (A5) | |
|---|---|
| TITLE | “SGRC2” in the first 5 columns |
| Control data (4I5) | |
| NELEM | Number of elements |
| ISPSMAS | 0 |
| INSIG | = 0 → No initial stress = 1 or 2 → Initial stresses |
| INBIO | = 0 → No Biot coefficient = 1 → Isotropic Biot coefficient = 2 → Anisotropic Biot coefficient Only for orthotropic mechanical law ORTHOPLA |
| Initial stresses - Only if INSIG > 0 (4G10.0) | |
| If INSIG=1: $\sigma_y=\sigma_{y0}+yd\sigma_{y}$ If INSIG=2: $\sigma_y=min(\sigma_{y0}+yd\sigma_y,0)$ |
|
| SIGY0 | $\sigma_{y0}$ effective stress $\sigma_y$ at the axes origin |
| DSIGY | Effective stress gradient along Y axis |
| AK0X | $k_0$ ratio $\sigma_x/\sigma_y$ |
| AK0Z | $k_0$ ratio $\sigma_z/\sigma_y$ (if AK0Z=0, AK0Z=AK0X) |
| Biot coefficient - Only if INBIO > 0 (3G10.0) | |
| See CSOL2 for more details | |
| If INBIO = 1 | |
| CBIOT | Biot coefficient |
| If INBIO = 2 | |
| CBIOT1 | Biot coefficient $b_{11}$ |
| CBIOT2 | Biot coefficient $b_{22}$ |
| CBIOT3 | Biot coefficient $b_{33}$ |
| Definition of the elements (5I5/9I5) | |
| NINTE | Number of integration points (1, 4, or 9) |
| LMATM | “Classic” mechanical law |
| LMATSG | “Second gradient” material law |
| LMATF | Fluid law |
| NNODF | Number of fluid nodes (4 or 8 - Default value = 8) |
| NODES(9) | List of nodes |
Results
Stresses (in global axes):
4 “classic” mechanical stresses: $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$
8 “second gradient” mechanical stresses: $\Sigma_{111}$, $\Sigma_{112}$, $\Sigma_{121}$, $\Sigma_{122}$, $\Sigma_{211}$, $\Sigma_{212}$, $\Sigma_{221}$, $\Sigma_{222}$
4 flow stresses: $f_x$, $f_y$, $f_{emmagasiné}$, $0$
Internal variables:
Internal variables of the “classic” mechanical law
Internal variables of the “second gradient” mechanical law
Internal variables of the fluid law
