/EOS/MURNAGHAN

Block Format Keyword Describes the Murnaghan equation of state.

Format

(1)	(3)	(5)	(7)	(9)
/EOS/MURNAGHAN/`mat_ID`/`unit_ID`
`eos_title`
`K`₀	`K`₁	`P`₀	`P`_sh	$ρ_{0}$

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)
`K`₀	Material parameter. (Real)	$[Pa]$
`K`₁	Material parameter. (Real)
`P`₀	Initial pressure. (Real)	$[Pa]$
`P`_sh	Pressure shift. (Real)	$[Pa]$
$ρ_{0}$	Reference density. Default = material density (Real)	$[\frac{kg}{m^{3}}]$

Example

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDPLA/7
IDEAL-GAS
#              RHO_I               RHO_0
             1.22e-3             1.22e-3
#                  E                  nu
                   0                   0
#                  a                   b                   n             eps_max           sigma_max
                1E30                   0                   0                   0                   0
#               Pmin 
                   0
/EOS/MURNAGHAN/7
NaCl  
#                 K0                  K1                  P0                 PSH                RHO0      
                24.0               5.390                 1.0                   0            2.165e-3
/ALE/MAT/7

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

This equation of state is also known as Tait Equation of State.(1)
$P (V) = \frac{K_{0}}{K_{1}} [{(\frac{V}{V_{0}})}^{- K_{1}} - 1]$

Where K₀ and K₁ are material parameters.
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)

¹ Murnaghan, F. D. "The compressibility of media under extreme pressures." Proceedings of the National Academy of Sciences 30, no. 9 (1944): 244-247