/EOS/LINEAR
Block Format Keyword Describes the linear equation of state $P\left(\mu \right)={P}_{0}+B\mu $ with initial pressure and bulk modulus.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/EOS/LINEAR/mat_ID/unit_ID  
eos_title  
${P}_{0}$  B  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) 

${P}_{0}$  Initial
pressure. (Real) 
$\left[\text{Pa}\right]$ 
B  Bulk
modulus. (Real) 
$\left[\text{Pa}\right]$ 
P_{sh}  Pressure
shift. (Real) 
$\left[\text{Pa}\right]$ 
${\rho}_{0}$  Reference
density. (Real) 
$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$ 
Example
#12345678910
/UNIT/1
unit for mat
kg m s
#12345678910
/MAT/LAW06/7/1
law06
# RHO_I
2.33e3
# NU PMIN
0.22 0.02
/EOS/LINEAR/7/1
linear EOS (Artificial data)
# P0 B PSH RHO0
1 10.0 0.0 2.33e3
/ALE/MAT/7
# Flrd
0
#12345678910
#enddata
Comments
 Linear EOS has the following
form:
(1) $$P\left(\mu \right)={P}_{0}+B\mu $$Where,(2) $$\mu =\frac{\rho}{{\rho}_{0}}1$$which can be derived from a polynomial EOS:(3) $$P={C}_{0}+{C}_{1}\mu +{C}_{2}{\mu}^{2}+{C}_{3}{\mu}^{3}+\left({C}_{4}+{C}_{5}\mu \right){E}_{0}$$Where, ${C}_{0}={P}_{0}$
 ${C}_{1}=B$
 ${C}_{2}={C}_{3}={C}_{4}={C}_{5}=0$
 Bulk modulus is usually
estimated as:
(4) $$B={\rho}_{0}\cdot {c}_{0}{}^{2}$$Where, ${c}_{0}$ is the initial sound speed.
 P_{sh} parameter enables to shift output pressure. Output pressure will also be a relative pressure $\text{\Delta}P\left(\mu \right)=P{P}_{sh}$ .
 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)