====== EHMIC ======
Plane or axisymmetric state
===== Description =====
{{  :elements:ehmic2.png?400|}}
2D Multi-scale Coupled Analysis in large deformations: Mechanical-Water-Air. \\
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Type: 283 \\
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The element is defined by 8 nodes indicated in NODES according to the order presented in the figure. 4 integration points are used for the interpolation. \\
The mechanical constitutive laws that can be used with this element are, for instance:
  * [[laws:ela|ELA]]: Elastic constitutive law
  * [[laws:epplasol|EP-PLASOL]]: Elasto-plastic constitutive law with linear elasticity
  * [[laws:orthopla|ORTHOPLA]]: Elasto‑plastic constitutive law with linear anisotropic elasticity
The flow constitutive laws that can be used with this element are, for now:
  * [[laws:hmic|HMIC]]: Hydraulic micro law with WA coupling and implicit mechanics
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Implemented by: F. Bertrand & G. Corman (2019)
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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: EHMICA.F  \\
Lagamine: EHMICB.F

===== Input file =====
^Title (A5)^^
|TITLE|"EHMIC" in the first 5 columns|
^Control data (4I5)^^
|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 (6I5/16I5(/9I5)) ^^
|NNODM|Number of nodes for the mechancial description: 8|
|NINTM|Number of integration point for the mechanical description: 4|
|LMATM|Mechanical law|
|NNODP|Number of nodes for the flow description: 8|
|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 hydraulic micro-elements in the microstructure (1I5/4I5) ^^
|NUMEL2|Number of hydraulic micro-elements|
|IELEM2|No. of the hydraulic micro-element|
|ILAW|Type of element: 1=bedding plane, 2=bundle of tubes, 3=bridging plane|
|NDUN|No. of the micro-node at one side of the micro-element|
|NDDEUX|No. of the micro-node at the other side of the micro-element|
^Definition of the hydraulic micro-nodes in the microstructure (1I5/10I5) ^^
|NUMNDH|Number of hydraulic micro-nodes|
|INOD2|No. of the hydraulic micro-node|
|IEDGE|No. of the microstructure boundary to which belong the micro-node: 0=none, 1=left or bottom, 2=right or top|
|IELUN|No. of the 1st micro-element connected to the micro-node|
|IELDEUX|No. of the 2nd micro-element connected to the micro-node|
|IELTROIS|No. of the 3rd micro-element connected to the micro-node|
|IELQUTR|No. of the 4th micro-element connected to the micro-node|
|IELCINQ|No. of the 5th micro-element connected to the micro-node|
|IELSIX|No. of the 6th micro-element connected to the micro-node|
|IELSEPT|No. of the 7th micro-element connected to the micro-node|
|IELHUIT|No. of the 8th micro-element connected to the micro-node|
===== Results =====
  * Stresses (in global axes)
    * Mechanical stresses $\sigma_x$, $\sigma_y$, $\sigma_{xy}$, $\sigma_z$ 
    * Flow in water $f_{wx}$, $f_{wy}$, $f_{w,stored}$
    * Flow in air $f_{ax}$, $f_{ay}$, $f_{a,stored}$
    * Advection dissolved gas flux $f_{adx}$, $f_{ady}$
    * Diffusion dissolved gas flux $f_{addx}$, $f_{addy}$
    * Advection gaseous gas flux $f_{agx}$, $f_{agy}$
  * Internal variables:
    * Internal variables of the mechanical law
    * Internal variables of the flow law