====== THNL-S ======

===== Description =====
Thermal conduction constitutive law for solid elements at variable temperature. \\

==== The model ====
Non linear thermal analysis of isotropic solids. \\
This constitutive law takes account of heat transfer by conduction and heat accumulation in solids, the conductivity and heat capacity of which depend on temperature. This law is used for two or three dimensional heat flow.
==== Files ====
Prepro: LTHNLS.F \\
Lagamine: THNL2.F (2D), THNL3.F (3D)
==== Subroutines ====

^File^Subroutine^Description^
|THNL2.F| THNL2|Main subroutine of the law for the 2D case|
|THNL3.F| THNL2|Main subroutine of the law for the 3D case|
===== 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| 100|
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (3I5) ^^
|NTEMP|= Number of temperatures at which material data are given|
|:::|= 0 Parameters expressed as a polynomial function of the temperature (only available for 3D case)|
|IENTH |= 0 to use the classical formulation of the heat problem|
|:::|= 1 to use the enthalpy formulation of the heat problem|
|:::|= 10 to use the enthalpy formulation of the heat problem and to define $\rho c(T)$ and not $\int \rho cdT$ that is performed by the Lagapre.|
|LOIM| = type number of the mechanical law in case of coupled analysis (for Levt2: 230, for [[laws:arbth|ARBTH]]: 250)|
==== Real parameters ====
=== If NTEMP > 0 ===

^ Line 1 (3G10.0) - repeated NTEMP times ^^
|T | Temperature|
|ALAMB | Heat conductivity at temperature T|
|RHOC |If IENTH = 0 or 10 → Heat capacity per unit volume at temperature T|
|:::|If IENTH = 1 → Enthalpy at temperature T, if IENTH = 1|

=== If NTEMP = 0 (only available for 3D case) ===
^Line 1 (2G10.0)^^
|Tmin | minimum temperature for the validity of the polynomial function|
|Tmax | maximum temperature for the validity of the polynomial function|
^Line 2 (4G10.0)^^
|AK|conductivity=AK*T<sup>3</sup>+BK*T<sup>2</sup>+CK*T+DK|
|BK|:::|
|CK|:::|
|DK|:::|
^Line 3 (3G10.0)^^
|ACAP| If IENTH = 0 → $\rho C_p = a_{CAP}T^2+b_{CAP}T+c_{CAP}$ \\ If IENTH = 1 → $\int{\rho C_p} = a_{CAP}T^2+b_{CAP}T+c_{CAP}$ \\ If IENTH = 10 → $\rho C_p = a_{CAP}T+b_{CAP}$|
|BCAP |:::|
|CCAP| :::|

===== Stresses =====
==== Number of stresses ====
5 for 3D state \\ 4 for the other cases
==== Meaning ====
__For the 3-D state:__
|SIG(1)|Conductive heat flow in the X direction (= $q_X$)|
|SIG(2)|Conductive heat flow in the Y direction (= $q_Y$)|
|SIG(3)|Conductive heat flow in the Z direction (= $q_Z$)|
|SIG(4)|Energy accumulated by heat capacity|
|SIG(5)|Heat power generated by plastic strains in case of coupled thermo-mechanical analysis.|

__For the other cases:__
|SIG(1)|Conductive heat flow in the X direction (= $q_X$)|
|SIG(2)|Conductive heat flow in the Y direction (= $q_Y$)|
|SIG(3)|Energy accumulated by heat capacity|
|SIG(4)|Heat power generated by plastic strains in case of coupled thermo-mechanical analysis.|


===== State variables =====
==== Number of state variables ====
1
==== List of state variables ====
In case of semi-coupled analysis:
|Q(1→X)|Mechanical state variable|
|Q(X+1)|RHOC|