/EOS/OSBORNE

Format

(1)	(3)	(5)	(7)	(9)
/EOS/OSBORNE/`mat_ID`/`unit_ID`
`eos_title`
`A`₁	`A`₂	`B`₀	`B`₁	`B`₂
`C`₀	`C`₁	`D`₀	`P`₀

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)
`A`₁	Osborne parameter. (Real)	$[P a^{2}]$ $[P a^{2}]$
`A`₂	Osborne parameter. (Real)	$[P a^{2}]$ $[P a^{2}]$
`B`₀	Osborne parameter. (Real)	$[Pa]$ $[Pa]$
`B`₁	Osborne parameter. (Real)	$[Pa]$ $[Pa]$
`B`₂	Osborne parameter. (Real)	$[Pa]$ $[Pa]$
`C`₀	Osborne parameter. (Real)
`C`₁	Osborne parameter. (Real)
`D`₀	Osborne parameter. (Real)	$[Pa]$ $[Pa]$
`P`₀	Initial pressure. (Real)	$[Pa]$ $[Pa]$

Table of Parameters

Here is a table of parameters for various material in unit system {g, cm, µs}

Material	$ρ_{0}$ $ρ_{0}$	$A_{1}$ $A_{1}$	$A_{2}$ $A_{2}$	$B_{0}$ $B_{0}$	$B_{1}$ $B_{1}$	$B_{2}$ $B_{2}$	$C_{0}$ $C_{0}$	$C_{1}$ $C_{1}$	$D_{0}$ $D_{0}$
Beryllium	1.845	0.9512	0.3453	0.9269	2.9484	0.5080	0.5644	0.6204	0.8
Boron	2.34	1.8212	4.3509	0.3764	0.3287	1.0801	0.5531	0.6346	.25
Graphite	2.25	0.1608	0.1619	0.8866	0.5140	1.4377	0.5398	0.5960	0.5
Magnesium	1.735	0.5665	0.3343	2.2178	0.8710	0.4814	0.4163	0.5390	1.5
Titanium	4.51	1.9428	0.6591	1.8090	2.6115	1.7984	0.4003	0.5182	1.8
Water	1.00	0.000384	0.001756	0.01312	0.06265	0.21330	0.5132	0.6761	0.02
Plexiglas	1.18	0.006199	0.015491	0.14756	0.05619	.050504	0.5575	0.6151	0.1
Polystyrene	1.04	0.038807	0.043646	0.77420	0.03610	0.46048	0.5443	0.6071	0.5
Polyethylene	0.913	0.007841	0.009766	0.19257	0.10257	0.31592	0.5748	0.6230	0.1
Micarta	1.39	0.016164	0.023579	0.34261	0.15107	0.43434	0.0540	0.0612	0.15
Silastic	1.43	0.004794	0.04684	0.33969	0.02377	0.50767	0.4925	0.5721	0.3
Aluminum	2.702	1.1867	0.7630	3.4448	1.5451	0.96430	0.43382	0.54873	1.5
Copper	8.90	4.9578	3.6884	7.4727	11.519	5.5251	0.39493	0.52883	3.6
Iron	7.86	7.78	31.18	9.591	15.676	4.634	0.3984	0.5306	9.0
Tungsten	19.17	21.67419	14.93338	10.195827	12.263234	9.6051515	0.33388437	0.48248861	7.0
Steel	7.9	4.9578323	3.6883726	7.4727361	11.519148	5.521138	0.39492613	0.52883412	3.6
Uranium	2.806	2.4562457	3.6883726	7.47361	11.519148	5.521138	0.39492613	0.52883412	0.6

▸Example (Aluminum)

#RADIOSS STARTER
/UNIT/1
unit for mat
                   g                  cm                 mus
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDPLA/7/1
ALUMINUM-JCOOK
#              RHO_I               RHO_0
               2.702               2.702
#                  E                  nu
                .734                0.33
#                  a                   b                   n             eps_max           sigma_max
               .0024               .0042                  .8                   0              .00680
#               Pmin                 Psh
              -.0223                   0
/EOS/OSBORNE/7/1
OSBORNE-EOS-ALUMINUM
#                 A1                  A2                  B0                  B1                  B2          
              1.1867              0.7630              3.4448              1.5451             0.96430 
#                 C0                  C1                  D0                  P0                  
             0.43382             0.54873                 1.5                 0.1                   
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/END
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

This equation of state is due to R.K. Osborne:(1)
$P (μ, E) = \frac{A_{1} μ + A_{2} μ | μ | + (B_{0} + B_{1} μ + B_{2} μ^{2}) E + (C_{0} + C_{1} μ) E^{2}}{E + D_{0}}$ $P (μ, E) = \frac{A_{1} μ + A_{2} μ | μ | + (B_{0} + B_{1} μ + B_{2} μ^{2}) E + (C_{0} + C_{1} μ) E^{2}}{E + D_{0}}$

Where,

$E$ $E$

Internal energy by initial volume

$E = \frac{E_{i n t}}{V_{0}} = ρ_{0} e$ $E = \frac{E_{i n t}}{V_{0}} = ρ_{0} e$

$μ$ $μ$

$\frac{ρ}{ρ_{0}} - 1$ $\frac{ρ}{ρ_{0}} - 1$

$A_{1}, A_{2}, B_{0}, B_{1}, B_{2}, C_{0}, C_{1}, D_{0}$ $A_{1}, A_{2}, B_{0}, B_{1}, B_{2}, C_{0}, C_{1}, D_{0}$

Constant parameters
Initial pressure is used to compute $E_{0}$ $E_{0}$ such that $P (0, E_{0}) = P_{0}$ $P (0, E_{0}) = P_{0}$ .
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)