/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 ) = i = 1 5 A i ( 1 λ R i v ) e R i v + λ E v + C ( 1 λ ω ) v ( ω 1 )
(2)
λ = ω + i = 1 5 ( A λ i v + B λ i ) e R λ i v

Where, v = 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) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW97/mat_ID/unit_ID or /MAT/JWLB/mat_ID/unit_ID
mat_title
ρ i ρ 0            
P0 psh       IIBFRAC
D PCJ E0 ω C
A5 A2 A3 A4 A5
R1 R2 R3 R4 R5
AL1 AL2 AL3 AL4 AL5
BL1 BL2 BL3 BL4 BL5
RL1 RL2 RL3 RL4 RL5

Definition

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)

[ kg m 3 ]
ρ 0 Reference density used in E.O.S (equation of state).

Default = ρ 0 = ρ i (Real)

[ kg m 3 ]
P0 Initial pressure

(Real)

[ Pa ]
Psh Pressure shift

(Real)

[ Pa ]
IBFRAC Burn fraction calculation flag.
= 0 (Default)
Volumetric Compression + Burning Time.
= 1
Volumetric Compression only.
= 2
Burning Time only.

(Integer)

 
D Detonation velocity.

(Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
PCJ Chapman Jouguet pressure.

(Real)

[ Pa ]
E0 Detonation energy per unit volume.

(Real)

[ J m 3 ]
ω Parameter of equation of state.

(Real)

 
C Parameter of equation of state.

(Real)

[ Pa ]
A1~A5 Parameter of equation of state.

(Real)

[ Pa ]
R1~R5 Parameter of equation of state.

(Real)

 
AL1~AL5 Parameter of equation of state.

(Real)

 
BL1~BL5 Parameter of equation of state.

(Real)

 
RL1~RL5 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
E0 .086116 .090798 .096034 .093757
D .83460 .85173 .85381 .84120
PCJ .30502 .32416 .33755 .32528
A1 909.13 909.14 909.17 549.98
A2 10.513 10.195 8.9469 5.8075
A3 .92253 .76191 .81495 .041638
R1 16.661 16.266 15.941 15.323
R2 5.9113 5.6415 5.4178 4.0477
R3 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

  1. JWLB EOS is an updated model from JWL EOS. For further information about JWL parameters, refer to /MAT/LAW5 (JWL).
  2. 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.