====== FMILC ======
===== Description =====
Constitutive law for mixed limit condition for element [[elements:fmilc|FMILC]]

==== The model ====
This law is only  used for non linear thermal analysis of solids. This constitutive law allows to impose a mixed limit condition on a boundary, with a classical penalty method.

==== Files ====
Prepro: LFMILC.F \\

===== Availability =====
|Plane stress state| YES |
|Plane strain state| YES |
|Axisymmetric state| YES |
|3D state| YES |
|Generalized plane state| YES |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 124 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (I5) ^^
|IDDL|DDL number (3 = water, 4 = air, 5 = temperature, in 2D case)|
|:::|DDL number (4 = water, 5 = air, 6 = temperature, in 3D case)|


==== Real parameters ====
^ Line 1 (1G10.0) ^^
|COEFK|K penalty coefficient|

===== Stresses =====
==== Number of stresses ====
1
==== Meaning (numerical, not physical) ====
|SIG(1)|= output or input flow at the boundary : \\ if $V_S < V_0$ : $q=0$ \\  if $V_S > V_0$ : $q=K\left(  V_0 - V_S \right) $|

{{:laws:v_q_garphic.png?400|}}

Where $V$ is either a pressure or a temperature, $V_0$ is the $V$ value of the environment node and $V_S$ is the V value of the integration point. 


===== State variables =====
==== Number of state variables ====
3
==== List of state variables ====
|Q(1)|water pressure (IDDL= 3 (in 2D) or 4 (in 3D)) \\ or gas pressure (IDDL= 4 (in 2D) or 5 (in 3D)) \\ or temperature (IDDL= 5, (in 2D) or 6 (in 3D)) of the solid at the integration point under consideration (=$V_S$) |
|Q(2)|reference water pressure (IDDL= 3 (in 2D) or 4 (in 3D)) \\ or reference gas pressure (IDDL= 4 (in 2D) or 5 (in 3D)) \\ or reference temperature (IDDL=5 (in 2D) or 6 (in 3D) (=$V_0$) |
|Q(3)| = $q$ |