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====== SGRC2 ======
Plane or axisymmetric state
===== Description =====
{{  :elements:sgra2.png?370|}}
Mechanical-flow analysis, Grenoble 2<sup>nd</sup> 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)((Pardoen, B. (2015). Hydro-mechanical analysis of the fracturing induced by the excavation of nuclear waste repository galleries using shear banding. PhD thesis, University of Liège. https://orbi.uliege.be/handle/2268/188222)).
==== 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 [[laws:orthopla|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 [[elements:csol2|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
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