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SGRT2
Plane or axisymmetric state
Description
Coupled Mechanical-Water-Air-Temperature analysis, Grenoble 2nd gradient method, in large deformations.
Type: 230
The element is defined by 9 nodes specified in NODES in the order indicated in the figure.
Nodes 1, 3, 5, and 7 have 9 DoF ($u_1$, $u_2$, $p_w$, $p_g$, $T$, $v_{11}$, $v_{12}$, $v_{21}$, $v_{22}$), whereas nodes 2, 4, 6, and 8 only have 5 DoF ($u_1$, $u_2$, $p_w$, $p_g$, $T$). 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 (water, air, temperature) description can be different from the mechanical description: the pressure/temperature can be linearly interpolated in a 4-nodes configuration, while the mechanical DoFs are parabolically interpolated in an 8-nodes configuration. In that case, the flow DoF must be fixed for the nodes that are not used (2, 4, 6, and 8).
The fluid constitutive laws that can be used with this element are, for now:
- WAVAT2: MWA coupling: Mechanical - Water - Air
Implemented by: G. Corman, H. Song (2019)
The framework definition of this element can be found in Corman (2024)1).
Files
Prepro: SGRT2A.F
Lagamine: SGRT2B.F
Input file
| Title (A5) | |
|---|---|
| TITLE | “SGRT2” 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) | |
| NNODM | Number of nodes for the mechancial description: 4 or 8 - Default value = 8 |
| NINTM | Number of integration points for the mechanical description: 1, 4, or 9 |
| LMATM | Classic (1st gradient) mechanical law |
| LMATSG | Second gradient mechanical law |
| NNODP | Number of nodes for the flow description: 4 or 8 - Default value = 8 |
| NINTP | Number of integration points for the flow description: 1, 4, or 9 Must be equal to NINTM |
| LMATF | Fluid law |
| NNODF | Number of fluid nodes (4 or 8 - Default value = 8) |
| NODES(9) | List of nodes |
Results
- Stresses (in global axxes)
- Mechanical stresses (4): $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$
- Flow in water (4): $f_{wx}$, $f_{wy}$, $f_{w,stored}$, 0
- Flow in air (4): $f_{ax}$, $f_{ay}$, $f_{a,stored}$, 0
- Thermal flow (4): $f_{tx}$, $f_{ty}$, $f_{t,stored}$, 0
- Internal variables:
- Internal variables of the (1st gradient) mechanical law
- Internal variables of the second gradient mechanical law
- Internal variables of the flow law
