====== FAIN2D ======
Interface 2D fault
===== Description =====
Type: 214 \\
\\
{{  :elements:faif2.png?400|}}
The element consists of 2, 3, 4, or 5 nodes (line, parabola - DoF 1, 2, 3) relating to one side of the fault (= the structure), and 2, 3, 4, or 5 additional nodes to discretize the flow  inside the fault (DoF 3). It also relates to a predefined foundation. \\
This element is dedicated to soil mechanics and in particular to structure-structure contact (fault). It includes pressure, friction, flow axial to the fault, and 2 flows transversal to the fault (along the thickness). \\ 
\\
Convention: when the element is considered in increasing order of nodes (1 → 2 → 3), the first body is to the left, and the tool or foundation to the right. \\ 
\\
This element can be used with mechanical law [[laws:intme|INTME2]] or a classic mechanical law and flow law [[laws:intec2|INTEC2]]. \\ 
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The element is compatible with plane stress state, plane strain state, and generalized plane state, as well as axisymmetric state. It can be used for mechanical, thermal, or thermo-mechanical analysis. \\ 
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__Warning__: When using renumbering of the DoFs, only directional renumbering works. \\
\\
Taken from [[elements:fail2|FAIL2]]

==== Files ====
Prepro: FAIN2A.F \\
Lagamine: FAIN2B.F

===== Input file =====
^Title (A5)^^
|TITLE|"FAIN2" in the first 5 columns|
^Control data (3I5)^^
|NELEM|Number of elements|
|INSIG|= 0  no initial stresses|
|:::  |= 1 or 2 → initial stresses|
|IDOMA|Number of the ES group to which the elements are connected (necessary in case of remeshing)|
^Initial stresses - only if INSIG = 1 ^^
|**If law = [[laws:intme|INTME2/INTME3]] (4G10.0)**||
|The pressure varies as: $PRESS = PRESS0 + (Y*DPRES) \text{ for } P\geq 0$ \\ Tau varies as: $TAU = TAU0+(Y*DTAU)$||
|PRES0|Pressure of the contact at the axis origin|
|DPRES|Coefficient of variation of the pressure along Y (= 0 → constant pressure)|
|TAU0|TAU at the axis origin|
|DTAU|Coefficient of variation of TAU along Y (= 0 → constant TAU)|
|**If law ≠ [[laws:intme|INTME2/INTME3]] (7G10.0)**||
|All stresses vary as: $SIGnn=SI0nn+(Y*DSIG)$||
|SI011|Stresses at the axis origin (y=0) \\ **expressed in local axes**|
|SI022|:::|
|SI012|:::|
|SI033|:::|
|DSIG|Coefficient of stress variation along Y ( = 0 → constant SIGnn)|
|DTAU|:::|
|RIGM|Penalty \\ = 1.0 by default \\ = 1/e inverse of the element thickness|
^Definition of the elements (6I5/10I5)^^
|NINTE|Number of integration points (1 to 10, 5 max can be drawn by DESFIN - recommanded value: 3)|
|LMATM|Mechanical law number|
|LMATF|Flow law|
|IFOND|Number of the foundation or tool \\ If the foundation number is equal to 0, the boundary thermal flow is calculated with the ambient, without mechanical contact with any foundation.|
|INTYP|Type of numerical integration (recommanded value: 0) \\ 0 → Gauss \\ 1 → Lobatto \\ 2 → Newton-Cote|
|IRIGF|Type of contact|
|:::| 0 → rigid foundation or tool |
|:::| 1 → uncoupled solid/solid contact \\ One contact element on each structure, the interpenetration distance is divided by 2. \\ Suitable for solids with similar stiffnesses.|
|:::| 2 → coupled solid/solid contact \\ Only one contact element must be defined on a solid, the other being its foundation. The computation of MBAND and NHICO must be actualized (see [[lagamex:auto#4th_line_14i5|ISTRA(4)]]). \\ Suitable for solids of different stiffnesses, with one (the foundation) can be more roughly approximated.|
|:::| 3 → coupled solid/solid contact \\ One contact element on each structure, the force is divided by 2. None of the structure is privileged. The computation of MBAND and NHICO must be actualized (see [[lagamex:auto#4th_line_14i5|ISTRA(4)]]). \\ Suitable for solids of different stiffnesses, both must be properly represented.|
|NODES(10)|List of nodes: 1, 2, (3), (4), (5), 1', 2', (3'), (4'), (5') \\ Nodes 3 and 3' can be 0; in that case the element is a straight line \\ Nodes 4 and 4' can be 0; in that case the element is a parabola \\ Nodes 5 and 5' can be 0; in that case the element is a cubic|

===== Results =====

__If the law is [[laws:intme|INTME2/INTME3]]:__ \\
**Stresses (20)**: 
  * Pressure
  * Tangent stress
  * 0
  * 0
  * Longitudinal flow, 
  * Stored flow, 
  * "FI" (between Foundation and Inside) transversal flow
  * "IS" (between Inside and Structure) transversal flow

__If the law is not [[laws:intme|INTME2/INTME3]]:__ \\
**Stresses**: 
  * $\sigma_{11}$, $\sigma_{22}$, $\sigma_{12}$, $\sigma_{33}$ in local axes
  * Longitudinal flow, Stored flow, "FI" (between Foundation and Inside) transversal flow, "IS" (between Inside and Structure) transversal flow

**Internal variables**: \\ 
The first values are the ones relating to the law \\ 
For [[laws:intme|INTME2/INTME3]], this will be: plasticity indicator, dissipation, fault closing $V$, fault opening $D$). 
\\ The 6 next values correspond to the contact geometry. They are: \\
  * The segment number of the foundation in contact
  * The interpenetration distance
  * The jacobian
  * NOCO the contact indicator given by CALFON
  * The relative tangent rate
  * The relative sliding
The last values are those relating to the flow law; for [[laws:intec2|INTEC2]], they are:
  * The pore pressure inside the fault
  * The longitudinal permeability
  * The transversal transmissivity