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

/EOS/MURNAGHAN/mat_ID/unit_ID  
eos_title  
K_{0}  K_{1}  P_{0}  P_{sh}  ${\rho}_{0}$ 
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) 

K_{0}  Material parameter. (Real) 
$\left[\text{Pa}\right]$ 
K_{1}  Material parameter. (Real) 

P_{0}  Initial pressure. (Real) 
$\left[\text{Pa}\right]$ 
P_{sh}  Pressure shift. (Real) 
$\left[\text{Pa}\right]$ 
${\rho}_{0}$  Reference density. Default = material density (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
Example
#12345678910
/UNIT/1
unit for mat
g mm ms
#12345678910
/MAT/HYDPLA/7
Articficial Linear Material Law
# RHO_I RHO_0
1.22e3 1.22e3
# E nu
0 0
# a b n eps_max sigma_max
1E30 0 0 0 0
# Pmin
0
/EOS/MURNAGHAN/7
EoS for NaCl at atmospheric pressure
# K0 K1 P0 PSH RHO0
24000 5.390 .1 0 2.165e3
/ALE/MAT/7
#12345678910
#enddata
Comments
 This equation of state is also known as Tait
Equation of State.
(1) $$\mathrm{P}\left(V\right)=\frac{{K}_{0}}{{K}_{1}}\left[{\left(\frac{V}{{V}_{0}}\right)}^{{K}_{1}}1\right]$$Where ${K}_{0}$ and ${K}_{1}$ are material parameters.
 This equation can also be found with
the following form:
(2) $$\frac{\text{\Delta}v}{{V}_{0}}=1{\left[1+\frac{{K}_{1}}{{K}_{0}}p\right]}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{1ex}{${K}_{1}$}\right.}$$With, $\text{\Delta}v={V}_{0}V$ and $p=P{P}_{0}$
 In some publications, the material parameters ${K}_{0}$ and ${K}_{1}$ are replaced by $c$ and $k$ with, ${K}_{0}=c$ and ${K}_{1}=c\times k$ .
 Another way to express this equation
is with the compressibility
$\mu $
.
(3) $$\mathrm{P}\left(\mu \right)={P}_{0}+\frac{{K}_{0}}{{K}_{1}}\left[{\left(1+\mu \right)}^{{K}_{1}}1\right]$$with $\mu =\frac{\rho}{{\rho}_{0}}1=\frac{{V}_{0}}{V}1$
 Murnaghan EOS does not depend on energy.
 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)