/EOS/GRUNEISEN
Block Format Keyword Describes the Gruneisen equation of state.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/EOS/GRUNEISEN/mat_ID/unit_ID  
eos_title  
C  S_{1}  S_{2}  S_{3}  
${\gamma}_{0}$  a  E_{0}  ${\rho}_{0}$ 
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) 

C  C sound speed. 1 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
S_{1}  S_{1}
material constant. 1 (Real) 

S_{2}  S_{2}
material constant. (Real) 

S_{3}  S_{3}
material constant. (Real) 

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

a  a coefficient (see
equation below). Default = ${\gamma}_{0}$ (Real) 

E_{0}  Initial energy per unit reference
volume. (Real) 
$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$ 
${\rho}_{0}$  Reference density. Default = material density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
Example (Copper)
#RADIOSS STARTER
#12345678910
/UNIT/1
unit for mat
g cm mus
#12345678910
/MAT/HYD_JCOOK/1/1
Copper (data from Example 46  TNT Cylinder Expansion Test)
# RHO_I RHO_0
8.96 0
# E nu
1.24 .35
# A B n epsmax sigmax
9E4 .00292 .31 0 .0066
# Pmin
1E30
# C EPS_DOT_0 M Tmelt Tmax
.025 1E6 1.09 1656 1E30
# RHOCP T_r
3.461E5 0
/EOS/GRUNEISEN/1/1
Copper
# C S1 S2 S3
.394 1.489 0 0
# GAMMA0 ALPHA E0 RHO_0
1.97 .47 0 8.96
#12345678910
#ENDDATA
Comments
 C, S_{1}, S_{2} and S_{3} are the coefficients of the cubic equation relating the shock velocity to the particle velocity.
 Let
$\mu =\frac{\rho}{{\rho}_{0}}1$
, if
$\mu >0$
, the pressure is given by:
(1) $$P=\frac{{\rho}_{0}{C}^{2}\mu \left[1+\left(1\frac{{\gamma}_{0}}{2}\right)\mu \frac{a}{2}{\mu}^{2}\right]}{{\left[1\left({S}_{1}1\right)\mu {S}_{2}\frac{{\mu}^{2}}{\mu +1}{S}_{3}\frac{{\mu}^{3}}{{\left(\mu +1\right)}^{2}}\right]}^{2}}+\left({\gamma}_{0}+a\mu \right)E$$  If
$\mu <0$
, the pressure is given by:
(2) $$P={\rho}_{0}{C}^{2}\mu +\left({\gamma}_{0}+a\mu \right)E$$  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)
 Input example with units: grams, cm,
$\mu s$
(microseconds):
Material ${\rho}_{0}\left[\frac{g}{c{m}^{3}}\right]$ $C\text{}\left[\frac{cm}{\mu s}\right]$ S_{1} ${\gamma}_{0}$ a Cu 8.9 0.394 1.489 1.97 0.47 Stainless Steel ^{1} 7.9 0.457 1.490 2.00 0.50 Al 2.7 0.533 1.338 2.18 0.48 Al Alloy ^{2} 2.7855 0.533 1.338 2.18 0.48 Be 1.8519 0.8 1.124 1.16 0.16 Mg Alloy ^{3} 1.7794 0.452 1.242 1.63 0.33 Ti 4.5249 0.47 1.146 1.3 0.20 Ni 8.8968 0.465 1.445 2 0.50 Pb 11.3379 0.201 1.54 2.84 0.54