/EOS/GRUNEISEN

Format

Definitions

Example (Copper)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/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
                9E-4              .00292                 .31                   0               .0066
#               Pmin
               -1E30
#                  C           EPS_DOT_0                   M               Tmelt               Tmax
                .025                1E-6                1.09                1656                1E30
#              RHOCP                                                         T_r
            3.461E-5                                                           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
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

1. C, S₁, S₂ and S₃ are the coefficients of the cubic equation relating the shock velocity to the particle velocity.
2. Let $\mu =\frac{\rho }{{\rho }_0}-1$ , if $\mu >0$ , the pressure is given by:(1)
   $$P=\frac{{\rho }_0{C}^2\mu \left[1+\left(1-\frac{{\gamma }_0}{2}\right)\mu -\frac{a}{2}{\mu }^2\right]}{{\left[1-\left(S_1-1\right)\mu -S_2\frac{{\mu }^2}{\mu +1}-S_3\frac{{\mu }^3}{{\left(\mu +1\right)}^2}\right]}^2}+\left({\gamma }_0+a\mu \right)E$$
3. If $\mu <0$ , the pressure is given by:(2)
   $$P={\rho }_0{C}^2\mu +\left({\gamma }_0+a\mu \right)E$$
4. 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 (HENSEL-SPITTEL)
5. Input example with units: grams, cm, $\mu s$ (micro-seconds):

   Material	${\rho }_0\left[\frac{g}{c{m}^3}\right]$	$C\left[\frac{cm}{\mu s}\right]$	S1	${\gamma }_0$	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