====== COU2DC/3DC ======
===== Description =====
Constitutive law for unilateral thermo-mechanical contact
==== The model ====
Thermo-mechanical analysis of problems involving unilateral contact between two bodies. Coulomb dry friction law is used. The contact condition is enforced via a penalty method or augmented Lagrangian method according to ISTRA(4). Heat transfer between the bodies depends upon the contact state. \\
  - Contact occurs(pression non zero) heat transfer is computed according the contact thermal resistance
  - Contact does not occur, heat transfer is computed by convection and radiation with constant coefficient.\\ In this case, the outside temperature is the following one :\\
    * INDIC = 1 always the atmosphere temperature
    * INDIC = 0 if the normal to the structure intersects one segment, this segment temperature is chosen; otherwise, the atmosphere temperature is used 
    * INDIC = 2 if the normal to the structure intersects one segment, this segment temperature is chosen; otherwise, no flux is computed (interest if 2 layers of contact element exist)
==== Files ====
Prepro: LCNTTH.F \\
Lagamine: COU2DC.F, COU3DC.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| 280|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing.|
==== Integer parameters ====
^ Line 1 (3I5) ^^
|INDIC| 0, 1, 2 to define the outside temperature used in case of no contact (see Use paragraph)|
|NINTV| 1 (except in 3D dynamic where value $\neq$ 1 is possible) \\ __For the 3D state dynamic analysis:__ \\ Number of sub-steps used to integrate numerically the constitutive equation in a time step|
|ISOL| 0, 1 or 4|
|NTEMP| Number of temperatures at which THCON, CONVEC & RADIA parameters are given (see hereafter). Default value = 1|
==== Real parameters ====
** if NTEMP = 1**
^Line 1 (7G10.0)^^
|AKP| penalty coefficient on the contact pressure $K_p$|
|AKTAU| penalty coefficient on the shear frictional stress $K_{\tau}$|
|PHI| COULOMB's friction coefficient $tg \phi $|
|B|cohesion|
|TAUMAX| maximum contact friction (only for 2D state) (default value = $10^{20}$)|
|THCON| thermal resistance when contact occurs|
|CONVEC|convection coefficient h|
^Line 2 (4G10.0)^^
|RADIA|radiation coeficient $\sigma_0$ $\varepsilon$ where $\sigma_0$ is the Boltzman constant, and  the $\varepsilon$ emissivity|
|CTQ| TAYLOR QUINNEY's coefficient to take into account the dissipation for heat computation \\ a. CTQ = -1 $\Rightarrow$ flux = QB(3) \\ b. CTQ $\in$ [0,1] $\Rightarrow$ QB(3) = $\Sigma (DISSIP/2*CTQ*\Delta t)$ \\ c. CTQ $\geq$ 100 $\Rightarrow$ flux = DISSIP/2*(CTQ-100) \\ Case a = semi-coupled analysis : thermal analysis \\ Case b = semi-coupled analysis : mechanical analysis \\ Case c = total coupled analysis|
|TAMB| atmosphere temperature|
|PRESID| residual pressure|
** if NTEMP > 1 **
^Line 1 (5G10.0)^^
|AKP| penalty coefficient on the contact pressure $K_p$|
|AKTAU| penalty coefficient on the shear frictional stress $K_{\tau}$|
|PHI| COULOMB's friction coefficient $\phi$|
|B| cohesion|
|TAUMAX| maximum contact friction (only for 2D state) (default value= $10^{20}$)|
^Line 2 (4G10.0) - Repeated NTEMP times^^
|TEMP|Temperature|
|THCON|Thermal resistance when contact occurs|
|CONVEC| convection coefficient h|
|RADIA|radiation coeficient $\sigma_0$ $\varepsilon$ where $\sigma_0$ is the Boltzman constant, and  the $\varepsilon$ emissivity|
^Line NTEMP+2 (3G10.0)^^
|CTQ| TAYLOR QUINNEY's coefficient to take into account the dissipation for heat computation \\ a. CTQ = -1 $\Rightarrow$ flux = QB(3) \\ b. CTQ $\in$ [0,1] $\Rightarrow$ QB(3) = $\Sigma (DISSIP/2*CTQ*\Delta t)$ \\ c. CTQ $\geq$ 100 $\Rightarrow$ flux = DISSIP/2*(CTQ-100) \\ Case a = semi-coupled analysis : thermal analysis \\ Case b = semi-coupled analysis : mechanical analysis \\ Case c = total coupled analysis|
|TAMB| atmosphere temperature|
|PRESID| residual pressure|


===== Stresses =====
==== Number of stresses ====
4 for 3D state \\ 3 for the other cases
==== Meaning ====
** For the 3D state **
|SIG(1)| normal contact pressure|
|SIG(2)| tangent contact stress in the $\xi$ direction|
|SIG(3)| tangent contact stress in the $\eta$ direction|
|SIG(4)| heat transfer|
The $\xi$ and $\eta$  correspond to the intrinsic co-ordinates of the contact element [[elements:cfi3d|CFI3D]] \\ \\
** For the other cases **
|SIG(1)| normal contact pressure|
|SIG(2)| tangent contact stress|
|SIG(3)| heat transfer|
===== State variables =====
==== Number of state variables ====
3
==== List of state variables ====
|Q(1)| 0 if the current state is elastic (no sliding)\\ 1 if the current state is elastoplastic (sliding at contact)\\ -1 no mechanical, nor thermical contact|
|Q(2)| amount of mechanical energy dissipated per unit area, due to friction|
|Q(3)| information concerning the mechanical dissipation into heat  flow (for exact meaning see CTQ parameter above)|