/EOS/OSBORNE
Block Format Keyword Describes the Osborne Equation of State from R.K. Osborne, also called the “quadratic EOS”.
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/EOS/OSBORNE/mat_ID/unit_ID | |||||||||
eos_title | |||||||||
A1 | A2 | B0 | B1 | B2 | |||||
C0 | C1 | D0 | P0 |
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) |
|
A1 | Osborne parameter. (Real) |
[Pa2] |
A2 | Osborne parameter. (Real) |
[Pa2] |
B0 | Osborne parameter. (Real) |
[Pa] |
B1 | Osborne parameter. (Real) |
[Pa] |
B2 | Osborne parameter. (Real) |
[Pa] |
C0 | Osborne parameter. (Real) |
|
C1 | Osborne parameter. (Real) |
|
D0 | Osborne parameter. (Real) |
[Pa] |
P0 | Initial pressure. (Real) |
[Pa] |
Table of Parameters
Material | ρ0 | A1 | A2 | B0 | B1 | B2 | C0 | C1 | D0 |
---|---|---|---|---|---|---|---|---|---|
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)
Comments
- This equation of state is due to R.K.
Osborne:
(1) P(μ,E)=A1μ+A2μ|μ|+(B0+B1μ+B2μ2)E+(C0+C1μ)E2E+D0Where,- E
- Internal energy by initial volume
- μ
- ρρ0−1
- A1,A2,B0,B1,B2,C0,C1,D0
- Constant parameters
- Initial pressure is used to compute E0 such that P(0,E0)=P0 .
- 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)