/EOS/OSBORNE
Block Format Keyword Describes the Osborne Equation of State from R.K. Osborne, also called the “quadratic EOS”.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/EOS/OSBORNE/mat_ID/unit_ID  
eos_title  
A_{1}  A_{2}  B_{0}  B_{1}  B_{2}  
C_{0}  C_{1}  D_{0}  P_{0}  
${\rho}_{0}$ 
Definition
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) 

A_{1}  Osborne parameter. (Real) 
$\left[\text{P}{\text{a}}^{2}\right]$ 
A_{2}  Osborne parameter. (Real) 
$\left[\text{P}{\text{a}}^{2}\right]$ 
B_{0}  Osborne parameter. (Real) 
$\left[\text{Pa}\right]$ 
B_{1}  Osborne parameter. (Real) 
$\left[\text{Pa}\right]$ 
B_{2}  Osborne parameter. (Real) 
$\left[\text{Pa}\right]$ 
C_{0}  Osborne parameter. (Real) 

C_{1}  Osborne parameter. (Real) 

D_{0}  Osborne parameter. (Real) 
$\left[\text{Pa}\right]$ 
P_{0}  Initial pressure. (Real) 
$\left[\text{Pa}\right]$ 
${\rho}_{0}$  Reference density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
Table of Parameters
Material  ${\rho}_{0}$  ${A}_{1}$  ${A}_{2}$  ${B}_{0}$  ${B}_{1}$  ${B}_{2}$  ${C}_{0}$  ${C}_{1}$  ${D}_{0}$ 

Beryllium  1.845  0.9512  0.3453  0.9269  2.9484  0.5080  0.5644  0.6204  0.8 
Boron  2.34  1.8212  4.3509  0.3764  0.3287  1.0801  0.5531  0.6346  .25 
Graphite  2.25  0.1608  0.1619  0.8866  0.5140  1.4377  0.5398  0.5960  0.5 
Magnesium  1.735  0.5665  0.3343  2.2178  0.8710  0.4814  0.4163  0.5390  1.5 
Titanium  4.51  1.9428  0.6591  1.8090  2.6115  1.7984  0.4003  0.5182  1.8 
Water  1.00  0.000384  0.001756  0.01312  0.06265  0.21330  0.5132  0.6761  0.02 
Plexiglas  1.18  0.006199  0.015491  0.14756  0.05619  .050504  0.5575  0.6151  0.1 
Polystyrene  1.04  0.038807  0.043646  0.77420  0.03610  0.46048  0.5443  0.6071  0.5 
Polyethylene  0.913  0.007841  0.009766  0.19257  0.10257  0.31592  0.5748  0.6230  0.1 
Micarta  1.39  0.016164  0.023579  0.34261  0.15107  0.43434  0.0540  0.0612  0.15 
Silastic  1.43  0.004794  0.04684  0.33969  0.02377  0.50767  0.4925  0.5721  0.3 
Aluminum  2.702  1.1867  0.7630  3.4448  1.5451  0.96430  0.43382  0.54873  1.5 
Copper  8.90  4.9578  3.6884  7.4727  11.519  5.5251  0.39493  0.52883  3.6 
Iron  7.86  7.78  31.18  9.591  15.676  4.634  0.3984  0.5306  9.0 
Tungsten  19.17  21.67419  14.93338  10.195827  12.263234  9.6051515  0.33388437  0.48248861  7.0 
Steel  7.9  4.9578323  3.6883726  7.4727361  11.519148  5.521138  0.39492613  0.52883412  3.6 
Uranium  2.806  2.4562457  3.6883726  7.47361  11.519148  5.521138  0.39492613  0.52883412  0.6 
Example (Aluminum)
#RADIOSS STARTER
/UNIT/1
unit for mat
g cm mus
#12345678910
/MAT/HYDPLA/7/1
ALUMINIUMJCOOK
# RHO_I RHO_0
2.702 2.702
# E nu
.734 0.33
# a b n eps_max sigma_max
.0024 .0042 .8 0 .00680
# Pmin Psh
.0223 0
/EOS/OSBORNE/7/1
OSBORNEEOSALUMINIUM
# A1 A2 B0 B1 B2
1.1867 0.7630 3.4448 1.5451 0.96430
# C0 C1 D0 P0
0.43382 0.54873 1.5 0.1
# RHO0
2.702
#12345678910
/END
#12345678910
Comments
 This equation of state is due to R.K.
Osborne:
(1) $$\mathrm{P}\left(\mu ,E\right)=\frac{{A}_{1}\mu +{A}_{2}\mu \left\mu \right+\left({B}_{0}+{B}_{1}\mu +{B}_{2}{\mu}^{2}\right)E+\left({C}_{0}+{C}_{1}\mu \right){E}^{2}}{E+{D}_{0}}$$Where, $E$
 Internal energy by initial volume
 $\mu $
 $\frac{\rho}{{\rho}_{0}}1$
 ${A}_{1},{A}_{2},{B}_{0},{B}_{1},{B}_{2},{C}_{0},{C}_{1},{D}_{0}$
 Constant parameters
 Initial pressure is used to compute ${E}_{0}$ such that $\mathrm{P}\left(0,{E}_{0}\right)={P}_{0}$ .
 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)