====== EHYPOFE2 ======
Plane or axisymmetric state
===== Description =====
{{  :elements:ehmic2.png?400|}}
2D Multi-scale Coupled Analysis:\\  Water-Air-Pollutant. \\
\\
Type: 284 \\
\\
The element is defined by 4 or 8 nodes indicated in NODES according to the order presented in the Figure. 4 integration points are used for the interpolation. \\
Remark: the convergence is better with 4 nodes than with 8 due to numerical oscillations.\\
The mechanical constitutive laws that can be used with this element are, for instance:
  * [[laws:ela|ELA]]: Elastic constitutive law
\\ 
Implemented by: A. Fanara based on the work of F. Bertrand, 2020
==== Files ====
Prepro: EHYPOFE2A.F  \\
Lagamine: EHYPOFE2B.F

===== Input file =====
^Title (A5)^^
|TITLE|"EHYPO"|

^Control data (2I5)^^
|NELEM|Number of elements|
|INSIG|= 0 → No initial stress \\ = 1 or 2 → Initial stresses|
^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)|
|The computation of SIGY0 and DSIGY must take into account the apparent specific mass, defined as \[\rho_a'=[(1-n)\rho_s+nS_w\rho_w]-\rho_w\] where: \\ $\rho_s$ is the solid specific mass - this represents the specific mass of a fictive sample where ther is no porosity, i.e. where the grains occupy the whole volume of the sample \\  $\rho_w$ is the fluid specific mass \\ $n$ is the porosity defined in the flow law related to the element \\ $S_w$ fluid saturation, ∈ [0,1]||

^Definition of the elements (6I5/4 or 8I5) ^^
|NNODM|Number of nodes for the mechanical description: 4 or 8 (preferred 4)|
|NINTM|Number of integration point for the mechanical description: 4|
|LMATM|Mechanical law|
|NNODP|Number of nodes for the fluid description: 4 or 8 (preferred 4)|
|NINTP|Number of integration points for the flow description: 4 \\ Must be equal to NINTM|
|LMATF|Flow law|
|NODES(NNODEM)|List of nodes|

^Definition of the elements in the microstructure ^^
^Line 1 (1I5) ^^
|NUMEL2|Total number of micro-elements|
^Line 2->NUMEL2+1 (6I5) ^^
|IELEM2|Number of the micro-element|
|ILAW|Type of element: 1=bedding plane, 2=bundle of tubes, 3=bridging plane|
|NDUN|No. of the micro-node at corner 1 of the micro-element|
|NDDEUX|No. of the micro-node at corner 2 of the micro-element|
|NDTROIS|No. of the micro-node at corner 3 of the micro-element|
|NDQUTR|No. of the micro-node at corner 4 of the micro-element|

===== Results =====
  * Stresses (in global axes)
    * Mechanical stresses $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$ 
    * Flow of water $f_{wx}$, $f_{wy}$, $f_{we}$
    * Flow of gas $f_{gx}$, $f_{gy}$, $f_{ge}$
    * Advective and diffusive flow of pollutant $f_{px}$, $f_{py}$, $f_{pe}$
    * Diffusion pollutant flux $f_{px,b},f_{py,b}$
  * Internal variables:
    * Internal variables of the mechanical law
    * Internal variables of the flow law