/EOS/TABULATED

Format

(1)	(3)	(5)
/EOS/IDEAL-GAS/`mat_ID`/`unit_ID`
`eos_title`
`fct_ID`_A	`Xscale`_A	`Fscale`_A
`fct_ID`_B	`Xscale`_B	`Fscale`_B
`E`₀	`P`_sh	$ρ_{0}$

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	(Optional) Unit identifier. (Integer, maximum 10 digits)
`eos_title`	EOS title. (Character, maximum 100 characters)
`fct_ID`_A	Function identifier for function A. Default = 0 (Integer)
`Xscale`_A	Scale factor for function A( $μ$ ) abscissa. Default = 1.0 (Real)
`Fscale`_A	Scale factor for function A( $μ$ ) ordinate. Default = 1.0 (Real)	$[Pa]$
`fct_ID`_B	Initial pressure. (Real)
`Xscale`_B	Scale factor for function B( $μ$ ) abscissa. Default = 1.0 (Real)
`Fscale`_B	Scale factor for function B( $μ$ ) ordinate. Default = 1.0 (Real)
`E`₀	Initial value for E. (Real)	$[Pa]$
`P`_sh	Pressure shift. (Real)	$[Pa]$
$ρ_{0}$	Reference density. Default = material density (Real)	$[\frac{kg}{m^{3}}]$

Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/BEGIN
Sample_for_air
      2022         0
                   g                  mm                  ms
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDRO/7/1
AIR
#              RHO_I               RHO_0
             1.22e-6                   0 
#                Knu                Pmin
              1.5E-2                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/ALE/MAT/7

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/EOS/TABULATED/7
Ideal Gas using  tabulated EoS P(µ)=A(µ)+B(µ)*E ; units {g,mm,ms} ; P(0)=0.1 MPa
#   A_func                       XscaleA             FscaleA
         0                             0                   0
#   B_func                       XscaleB             FscaleB
      1002                      1.000000            1.000000
#                 E0                 PSH                RHO0
                0.25                 0.1             1.22e-6
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/FUNCT/1002
EOS FUNCT - B(µ) = (GAMMA-1).(1+µ) ; where gamma=1.4 ; units {g,mm,ms}
#                  X                   Y
                  -1                 0.0                                                            
                   0                 0.4                                                           
                   9                 4.0 
                  99                40.0
                9999              4000.0                                                                              
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#ENDDATA
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

Tabulated EoS is defined with:(1)
$P = A (µ) + B (µ) E$

Where,

$μ$

is defined as $µ = \frac{ρ}{ρ_{0}} - 1$

$E$

is $ρ_{0} e$ (SI unit J/m³ or Pa)

$A$ and $B$

are user-defined functions
Optional scale factors are introduced such as:(2)
$P = F s c a l e_{A} . A (\frac{µ}{X s c a l e_{A}}) + F s c a l e_{B} . B (\frac{µ}{X s c a l e_{B}}) E$

$P (μ, E) = (γ - 1) (1 + μ) E$ with $γ = \frac{C_{p}}{C_{v}}$ and $C_{p}$ , $C_{v}$ are constant parameters.

Consequently, the same equation of state can be built using /EOS/IDEAL-GAS-VT (Volume Temperature) defining the special case of a constant function:(3)
$C_{p} (T) = \frac{γ r}{γ - 1}$
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 (HENSEL-SPITTEL)