/MAT/LAW97 (JWLB)

Block Format Keyword This law describes the Jones-Wilkins-Lee-Baker EOS for detonation products of high explosives.

(1)

P (v, E) = \sum_{i = 1}^{5} A_{i} (1 - \frac{λ}{R_{i} v}) e^{- R_{i} v} + \frac{λ E}{v} + C (1 - \frac{λ}{ω}) v^{- (ω - 1)}

(2)

λ = ω + \sum_{i = 1}^{5} (A_{λ i} v + B_{λ i}) e^{- R_{λ i} v}

Where, $v = \frac{V}{V_{0}}$ is relative volume and $E = ρ_{0} e$ and $A_{i}, R_{i}, A_{λ i}, B_{λ i}, R_{λ i}, ω, C$ are material parameters.

Format

(1)	(3)	(5)	(7)	(9)	(10)
/MAT/LAW97/`mat_ID`/`unit_ID` or /MAT/JWLB/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}$	$ρ_{0}$
`P`₀	`p`_sh				`II`_BFRAC
`D`	`P`_CJ	`E`₀	$ω$	`C`
`A`₅	`A`₂	`A`₃	`A`₄	`A`₅
`R`₁	`R`₂	`R`₃	`R`₄	`R`₅
`AL`₁	`AL`₂	`AL`₃	`AL`₄	`AL`₅
`BL`₁	`BL`₂	`BL`₃	`BL`₄	`BL`₅
`RL`₁	`RL`₂	`RL`₃	`RL`₄	`RL`₅

Definitions

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Interger, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
$ρ_{i}$	Initial density. (Real)	$[\frac{kg}{m^{3}}]$
$ρ_{0}$	Reference density used in E.O.S (equation of state). Default = $ρ_{0} = ρ_{i}$ (Real)	$[\frac{kg}{m^{3}}]$
`P`₀	Initial pressure (Real)	$[Pa]$
`P`_sh	Pressure shift (Real)	$[Pa]$
`I`_BFRAC	Burn fraction calculation flag. = 0 (Default) Volumetric Compression + Burning Time. = 1 Volumetric Compression only. = 2 Burning Time only. (Integer)
`D`	Detonation velocity. (Real)	$[\frac{m}{s}]$
`P`_CJ	Chapman Jouguet pressure. (Real)	$[Pa]$
`E`₀	Detonation energy per unit volume. (Real)	$[\frac{J}{m^{3}}]$
$ω$	Parameter of equation of state. (Real)
`C`	Parameter of equation of state. (Real)	$[Pa]$
`A`₁~`A`₅	Parameter of equation of state. (Real)	$[Pa]$
`R`₁~`R`₅	Parameter of equation of state. (Real)
`AL`₁~`AL`₅	Parameter of equation of state. (Real)
`BL`₁~`BL`₅	Parameter of equation of state. (Real)
`RL`₁~`RL`₅	Parameter of equation of state. (Real)

Example

#RADIOSS STARTER
#---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/LAW97/7/1
JWLB - OCTOL 72/25
#              RHO_I               RHO_0
               1.821               1.821
#                 P0                 PSH                                                      IBFRAC
                   0                   0                                                           0
#                  D                 PCJ                  E0                   W                   C
             0.85381              .33755             .096034              .30731            .0104772
#                 A1                  A2                  A3                  A4                  A5
              909.17              8.9469              .81495                   0                   0
#                 R1                  R2                  R3                  R4                  R5
              15.941              5.4178              2.1956                   0                   0
#                AL1                 AL2                 AL3                 AL4                 AL5
              65.093             -179.81              156.04              .78487                   0
#                BL1                 BL2                 BL3                 BL4                 BL5
                   0                   0                   0                   0                   0 
#                RL1                 RL2                 RL3                 RL4                 RL5                
              3.6906             4.52693              5.8014              .95864                   0
/ALE/MAT/7/1  
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Parameters

From Reference

Unit System is g, cm, ms, Mbar

	PAX2	PAX2A	OCTOL 77/25	OCTOL 70/30
$ρ_{0}$	1.7370	1.770	1.821	1.803
`E`₀	.086116	.090798	.096034	.093757
`D`	.83460	.85173	.85381	.84120
`P`_CJ	.30502	.32416	.33755	.32528
`A`₁	909.13	909.14	909.17	549.98
`A`₂	10.513	10.195	8.9469	5.8075
`A`₃	.92253	.76191	.81495	.041638
`R`₁	16.661	16.266	15.941	15.323
`R`₂	5.9113	5.6415	5.4178	4.0477
`R`₃	2.3618	2.1540	2.1956	.62665
`C`	.011724	.011325	.0104772	.0058269
$ω$	.35956	.36989	.30731	.27665
$A_{λ 1}$	46.898	69.018	65.093	1.5621
$A_{λ 2}$	-215.40	-176.03	-179.81
$A_{λ 3}$	270.22	163.48	156.04
$A_{λ 4}$	.88536	.76214	.78487
$B_{λ 1}$				-.27665
$R_{λ 1}$	4.3128	4.0339	3.6906	1.0841
$R_{λ 2}$	5.7197	4.8830	4.52693
$R_{λ 3}$	7.318	6.5455	5.8014
$R_{λ 4}$	1.0892	1.0394	.95864

Comments

JWLB EOS is an updated model from JWL EOS. For further information about JWL parameters, refer to /MAT/LAW5 (JWL).
JWLB EOS can be degenerated into JWL EOS using:
$n = 2$ ; C=0; $A_{λ i} = B_{λ i} = 0$

¹ Baker, Ernest L. Modeling and optimization of shaped charge liner collapse and jet formation. No. ARAED-TR-92019. ARMY ARMAMENT RESEARCH DEVELOPMENT AND ENGINEERING CENTER PICATINNY ARSENAL NJ ARMAMENT ENGINEERING DIRECTORATE, 1993.