/MAT/LAW18 (THERM)
Block Format Keyword This law describes thermal material.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW18/mat_ID or /MAT/THERM/mat_ID  
mat_title  
${\rho}_{i}$  ${\rho}_{0}$  
$\rho {\text{\hspace{0.05em}}}_{0}{C}_{p}$  A  B  
fct_ID_{T}  T_{0}  Fscale_{T}  
fct_ID_{sph}  fct_ID_{as}  Fscale_{sph}  Fscale_{E}  Fscale_{K} 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material
identifier (Integer, maximum 10 digits) 

mat_title  Material
title (Character, maximum 100 characters) 

${\rho}_{i}$  Initial
density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
${\rho}_{0}$  Reference density used in
E.O.S (equation of state). Default ${\rho}_{0}$ = ${\rho}_{i}$ (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
$\rho {\text{\hspace{0.05em}}}_{0}{C}_{p}$  Specific
heat (Real) 
$\left[\frac{\text{kg}}{{\text{s}}^{3}\cdot \text{m}\cdot \text{K}}\right]$ 
A  Conductivity coefficient
A (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
B  Conductivity coefficient
B (Real) 

fct_ID_{T}  Function
f(t) identifier for T. 9
(Integer) 

T_{0}  Initial
temperature Default = 300K (Real) 
$\left[\text{K}\right]$ 
Fscale_{T}  Time scale
factor (Real) 

fct_ID_{sph}  Function g(T, E)
identifier for temperature versus energy. 7 (Integer) 

fct_ID_{as}  Function h(k, T)
identifier for conductivity versus
temperature. (Integer) 

Fscale_{sph}  Temperature scale
factor. (Real) 
$\left[\text{K}\right]$ 
Fscale_{E}  Energy scale
factor. (Real) 
$\left[\text{J}\right]$ 
Fscale_{K}  Conductivity scale
factor. (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
Comments
 This material can be used:
 as purely thermal material (only Line 4 is read)
 as boundaries conditions (temperature or flux) (use Line 5)
 The
$k$
(thermal conductivity) is computed
as:
(1) $$k=A+B\cdot T$$  The α (thermal diffusivity) is computed as:
(2) $$\alpha =k/{\rho}_{0}{C}_{p}$$Where, ${C}_{p}$ is the heat capacity at constant pressure.
 The $k$ (thermal conductivity) is given by curve $fct\text{}\_\text{}I{D}_{as}=k(T)$ .
 The α (thermal diffusivity) is computed with curve fct_ID_{sph} $\alpha =k/{\rho}_{0}{C}_{p}$ with, $\frac{dE}{dT}={C}_{p}$ .
 Function g(T, E) is similar to
the following curve:
 If
fct_ID_{sph} ≠
0,
(3) $${E}_{specific}=\frac{\raisebox{1ex}{${E}_{\mathrm{int}}$}\!\left/ \!\raisebox{1ex}{${\rho}_{0}$}\right.}{Fscal{e}_{E}}$$$T={\mathrm{f}}_{sph}({E}_{specific})\cdot Fscal{e}_{sph}$
Where, ${\mathrm{f}}_{sph}$ is the function of fct_ID_{sph}.
 If
fct_ID_{sph} =
0,
(4) $$T=\frac{{E}_{\mathrm{int}}}{\mathit{sph}}$$with $Sph={\rho}_{0}{C}_{p}=SpecificHeat$
 If
fct_ID_{T} ≠
0,
(5) $$T=\mathrm{f}(Time)\cdot {T}_{0}$$with $Time=Time\cdot Fscal{e}_{T}$ ; ${E}_{\mathrm{int}}=T\cdot sph$ .
 If
fct_ID_{as} ≠ 0,
(6) $$T=\frac{T}{Fscal{e}_{sph}}$$$A={\mathrm{f}}_{as}\left(T\right)\cdot Fscal{e}_{E}$ ; $B=0$
Where, ${\mathrm{f}}_{as}$ is the function of fct_ID_{as}.