Thermal conduction constitutive law for solid elements at variable temperature.
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.
Prepro: LTHNLS.F
Lagamine: THNL2.F (2D), THNL3.F (3D)
| 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 |
| Plane stress state | YES |
| Plane strain state | YES |
| Axisymmetric state | YES |
| 3D state | YES |
| Generalized plane state | YES |
| Line 1 (2I5, 60A1) | |
|---|---|
| IL | Law number |
| ITYPE | 100 |
| COMMENT | Any comment (up to 60 characters) that will be reproduced on the output listing |
| 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 ARBTH: 250) |
| 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 | |
| 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*T3+BK*T2+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 | |
5 for 3D state
4 for the other cases
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. |
1
In case of semi-coupled analysis:
| Q(1→X) | Mechanical state variable |
| Q(X+1) | RHOC |