/MAT/LAW16 (GRAY)
Block Format Keyword This material law is based on Gray EOS and JohnsonCook yield criteria.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MAT/LAW16/mat_ID or /MAT/GRAY/mat_ID  
mat_title  
${\rho}_{i}$  ${\rho}_{0}$  
E  ν  
a  b  n  ${\epsilon}_{\mathrm{max}}$  ${\sigma}_{\mathrm{max}}$  
P_{0}  C  S  $\gamma $ _{0}  α_{e}  
AW  P_{min}  E_{0}  
c  ${\dot{\epsilon}}_{0}$  m  T_{melt}  T_{max}  
$\gamma $ _{0m}  α_{m}  $\gamma $ _{e}  g_{e}  $\text{\Delta}S$  
T_{m0}  V_{j}  V_{b}  
E_{oh}  A_{y}  $\theta $ 
Definition
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) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
E  Young's
modulus. (Real) 
$\left[\text{Pa}\right]$ 
ν  Poisson's
ratio. (Real) 

a  Plasticity yield
stress. (Real) 
$\left[\text{Pa}\right]$ 
b  Plasticity hardening
parameter. (Real) 
$\left[\text{Pa}\right]$ 
n  Plasticity hardening
exponent. Default = 1.0001 (Real) 

${\epsilon}_{\mathrm{max}}$  Failure plastic
strain. Default = 10^{30} (Real) 

${\sigma}_{\mathrm{max}}$  Plasticity maximum
stress. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
P_{0}  Initial
pressure. (Real) 
$\left[\text{Pa}\right]$ 
C  Hugoniot
parameters. (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
S 
${U}_{s}=C+S\hspace{0.17em}{U}_{p}$
(Real) 

$\gamma $ _{0}  Lattice
gamma. (Real) 

$\sigma $ _{e} 
$\gamma ={\gamma}_{0}a\hspace{0.17em}x$
(Real) 

AW  Atomic
weight. (Real) 
$\left[\frac{kg}{mole}\right]$ 
P_{min}  Pressure cutoff. Default = 10^{30} (Real) 
$\left[\text{Pa}\right]$ 
E_{0}  Initial energy per unit
volume. (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
c  Strain rate coefficient.
(Real) 

${\dot{\epsilon}}_{0}$  Reference strain rate
(time unit)^{1}. (Real) 
$\left[\frac{\text{1}}{\text{s}}\right]$ 
m  Temperature
exponent. Default = 1.0 (Real) 

T_{melt}  Melting
temperature. Default = 10^{30} (Real) 
$\left[\text{K}\right]$ 
T_{max}  For T >
T_{max}: m =1 is used. Default = 10^{30} (Real) 
$\left[\text{K}\right]$ 
$\gamma $ _{0m}  Melting gamma. Default = $\gamma $ _{0} (Real) 

$\sigma $ _{m} 
${\gamma}_{m}={\gamma}_{0m}{a}_{m}\hspace{0.17em}x$
Default = a (Real) 

$\gamma $ _{e}  Electronic
gamma. Default = 2/3 (Real) 

g_{e}  Electronic energy
coefficient. Default = 0.0 (Real) 
$\left[\frac{\text{J}}{\text{m}\text{o}\text{l}\text{e}\cdot {\text{K}}^{2}}\right]$ 
$\text{\Delta}S$  Entropy of
melting. Default = 9.637e+3 $\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$ (Real) If blank or 0, default entropy of melting value is automatically translated to the working units. 
$\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$ 
T_{m0}  Melting temperature
parameter. Default = 1.3 T_{melt} (Real) 
$\left[\text{K}\right]$ 
V_{j}  Volume where EOS are
joined. (Real) 
$\left[\frac{{\text{m}}^{3}}{\text{k}\text{g}}\right]$ 
V_{b}  Excluded volume for vapor
phase. Default = 0.5/r_{0} (Real) 
$\left[\frac{{\text{m}}^{3}}{\text{k}\text{g}}\right]$ 
E_{oh}  Energy at
V=V_{0},
T=300K,
P=0. Default = 0.0 (Real) 
$\left[\text{J}\right]$ 
A_{y}  Coefficient of attractive
potential. (Real) 
$\left[\frac{\mathrm{J}{\text{m}}^{3}}{{\text{mole}}^{2}}\right]$ 
$\theta $  Join parameter. Default = 1.0 (Real) 
Example (Aluminum)
#RADIOSS STARTER
#12345678910
/MAT/LAW16/1
Aluminium  GRAY EOS (unit g_cm_mus)
# RHO_I RHO_0
2.7 0
# E Nu
0.71 .33
# a b n Eps_max sigmax
0.002 0.00144 0.62 0 0
# P0 C S Gamma_0 a_e
0 0.533 1.338 2.18 1.7
# AW P_min E0
26.98 5e3
# c eps_dot_0 m T_melt T_max
1 1E30
# Gamma_0m a_m Gamma_e g_e delta_S
2.18 1.7 0.6667 8.7e9 9.637E5
# T_m0 V_j V_b
1220 0.47388 0.19025
# E_0h a_y Theta
0 47 1
#12345678910
#ENDDATA
#12345678910
Comment
 The correct model units must
be defined in the /BEGIN card because the default value of
$\text{\Delta}S$
entropy of melting is calculated based on the unit system.
(1) $$\begin{array}{cc}\sigma =\left(a+b{{\epsilon}_{p}}^{n}\right)\left(1+c\hspace{0.17em}\text{ln}\frac{\dot{\epsilon}}{{\dot{\epsilon}}_{0}}\right)\left(1{\left({T}^{*}\right)}^{m}\right)& {T}^{*}=\frac{T{T}_{0}}{{T}_{\mathit{melt}}{T}_{0}}\end{array}$$