/EOS/POLYNOMIAL

Format

(1)	(3)	(5)	(7)
/EOS/POLYNOMIAL/`mat_ID`/`unit_ID`
`eos_title`
`C`₀	`C`₁	`C`₂	`C`₃
`C`₄	`C`₅	`E`₀	`P`_sh

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)
`C`₀	Hydrodynamic pressure law coefficient. (Real)	$[Pa]$ $[Pa]$
`C`₁	Hydrodynamic pressure law coefficient. (Real)	$[Pa]$ $[Pa]$
`C`₂	Hydrodynamic pressure law coefficient. (Real)	$[Pa]$ $[Pa]$
`C`₃	Hydrodynamic pressure law coefficient. (Real)	$[Pa]$ $[Pa]$
`C`₄	Energy pressure law coefficient. (Real)
`C`₅	Energy pressure law coefficient. (Real)
`E`₀	Initial internal energy per unit reference volume. (Real)	$[\frac{J}{m^{3}}]$ $[\frac{J}{m^{3}}]$
`P`_sh	Pressure shift. (Real)	$[Pa]$ $[Pa]$

▸Example (Steel)

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/8
steel
#              RHO_I               RHO_O
                7.89                  0
#                 E                   nu
                 2.1                  .3
#                  A                   B                   n              epsmax              sigmax
                .011              .00275                 .36                   0                   0
#               Pmin
               1E-10
#                  C           EPS_DOT_0                   M               Tmelt                Tmax
                .022                1E-6                   1                1811                2000
#              RHOCP                                                         T_r
             3.57E-5                                                           0
/EOS/POLYNOMIAL/8
steel
#                 C0                  C1                  C2                  C3
                   0                1.69                 3.1                   0
#                 C4                  C5                  E0                 Psh               
                1.83                1.83                   0                   0                   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYD_JCOOK/9
tungstene
#              RHO_I               RHO_O
                17.6                   0
#                 E                   nu
                 3.6                  .3
#                  A                   B                   n              epsmax              sigmax
              .01506              .00177                 .12                   0                   0
#               Pmin
               1E-10
#                  C           EPS_DOT_0                   M               Tmelt                Tmax
                .016                1E-6                   1                3400                3400
#              RHOCP                                                         T_r
             2.36E-5                                                           0
/EOS/POLYNOMIAL/9
tungstene
#                 C0                  C1                  C2                  C3
                   0                2.82                   2               -1.37
#                 C4                  C5                  E0                 Psh               
                1.54                1.54                   0                   0                   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA

Comments

Pressure is defined by the linear polynomial:(1)
$P = C_{0} + C_{1} μ + C_{2} μ^{2} + C_{3} μ^{3} + (C_{4} + C_{5} μ) E$ $P = C_{0} + C_{1} μ + C_{2} μ^{2} + C_{3} μ^{3} + (C_{4} + C_{5} μ) E$

with (2)
$μ = \frac{ρ}{ρ_{0}} - 1$ $μ = \frac{ρ}{ρ_{0}} - 1$

and $E$ $E$ being the internal energy per unit reference volume.
If $μ < 0$ $μ < 0$ , then $C_{2} μ^{2} = 0$ $C_{2} μ^{2} = 0$ .
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 (HENSEL-SPITTEL)