/EOS/NOBLEABEL
Block Format Keyword Describes the covolume equation of state $P\left(vb\right)=RT$ .
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/EOS/NOBLEABEL/mat_ID/unit_ID  
eos_title  
b  $\gamma $  E_{0}  P_{sh}  ${\rho}_{0}$ 
Definitions
Field  Contents  SI Unit Example 

mat_ID  Material identifier. (Integer, maximum 10 digits) 

unit_ID  Unit Identifier. (Integer, maximum 10 digits) 

eos_title  EOS title. (Character, maximum 100 characters) 

b  Covolume. (Real) 
$\left[\frac{{m}^{3}}{kg}\right]$ 
$\gamma $  Heat Capacity ratio
$\gamma =\frac{{C}_{p}}{{C}_{v}}$
. (Real) 

E_{0}  Initial internal energy per unit
reference volume. (Real) 
$\left[\frac{J}{{m}^{3}}\right]$ 
P_{sh}  Pressure shift. (Real) 
$\left[\mathrm{Pa}\right]$ 
${\rho}_{0}$  Reference density. Default = material density (Real) 
$\left[\frac{kg}{{m}^{3}}\right]$ 
Example
#12345678910
/UNIT/1
unit for mat
g mm ms
#12345678910
/MAT/HYDPLA/7
NOBLE_ABEL
# RHO_I RHO_0
1.22e6 0
# E nu
0 0
# a b n eps_max sigma_max
1E30 0 0 0 0
# Pmin Psh
0
/EOS/NOBLEABEL/7
NOBLEABEL EOS
# b GAMMA E0 PSH RHO0
1E3 1.4 0.2499999997 0 1.22e6
/ALE/MAT/7
#12345678910
#enddata
Comments
 A generalization of the idealgas
thermal EOS,
$Pv=RT$
is the covolume equation of state
$P\left(vb\right)=RT$
Where,
 $v$
 Specific volume
 b
 Covolume
 R
 Specific gas constant
 T
 Temperature
Previous form $P=\mathrm{P}\left(v,T\right)$ , can be written in $P=\mathrm{P}\left(\mu ,E\right)$ form.
Where, $\mu =\frac{\rho}{{\rho}_{0}}1$
 $E=\frac{{E}_{int}}{{V}_{0}}$
 $\mathrm{P}\left(\mu ,E\right)=\frac{\left(\gamma 1\right)\left(1+\mu \right)E}{1b{\rho}_{0}\left(1+\mu \right)}$
with $\gamma =\frac{{C}_{p}}{{C}_{v}}$
 This EOS applies to dense gases at high pressure for which the volume occupied by the molecules themselves is no longer negligible.
 Covolume b is usually in range $\left[0.9\times {10}^{3},1.1\times {10}^{3}\right]$ $\left[\frac{{m}^{3}}{kg}\right]$
 Some comparison with ideal gas EOS:
IDEALGAS NOBLEABEL $\mathrm{P}\left(v,T\right)$ $Pv=RT$ $P\left(vb\right)=RT$ $\mathrm{P}\left(\mu ,E\right)$ $\left(\gamma 1\right)\left(1+\mu \right)E$ $\frac{\left(\gamma 1\right)\left(1+\mu \right)E}{1b{\rho}_{0}\left(1+\mu \right)}$ Sound Speed $c$
$c=\sqrt{\frac{\gamma P}{\rho}}$ $c=\sqrt{\frac{\gamma P}{\left(1b\rho \right)\rho}}$ ${E}_{0}=\mathrm{E}\left(0\right)$ $\frac{{P}_{0}}{\gamma 1}$ $\frac{{P}_{0}\left(1b{\rho}_{0}\right)}{\gamma 1}$  Equations of state are used by
Radioss to compute the hydrodynamic pressure and are
compatible with the material laws:
 /MAT/LAW3 (HYDPLA)
 /MAT/LAW4 (HYD_JCOOK)
 /MAT/LAW6 (HYDRO or HYD_VISC)
 /MAT/LAW10 (DPRAG1)
 /MAT/LAW12 (3D_COMP)
 /MAT/LAW49 (STEINB)
 /MAT/LAW102 (DPRAG2)
 /MAT/LAW103 (HENSELSPITTEL)