Lagamine

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====== SGRT2 ======
Plane or axisymmetric state
===== Description =====
{{ :elements:sgrt2.png?370|}}
Coupled Mechanical-Water-Air-Temperature analysis, Grenoble 2<sup>nd</sup> 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:
  * [[laws:wavat|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)((Corman, G. (2024). Hydro-mechanical modelling of gas transport processes in clay host rocks in the context of a nuclear waste repository. PhD thesis, University of Liège. https://hdl.handle.net/2268/307996)).
==== 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 [[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)^^
|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
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