/MAT/LAW41 (LEE-TARVER)

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/MAT/LAW41 - Lee-Tarver Material

Description

This material law describes detonation products using an ignition and growth model of a reactive material. The Lee–Tarver model is based on the assumption that ignition starts at local hot spots in the passage of shock front and grows outward from these sites. The reaction rate is controlled by the pressure and the surface area as in a deflagration process.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW41/mat_ID or /MAT/LEE-TARVER/mat_ID
mat_title

Ireac
Ar		Br
Ap		Bp
				EQ
itr				check
rki		ex		ri
rkg		yg		zg		ex1
k		X		tol
grow2		ex2		yg2		zg2
ccrit		fmxig		fmxgr		fmngr
G		Ti

Field	Contents	SI Unit Example
mat_ID	Material identifier (Integer, maximum 10 digits)
mat_title	Material title (Character, maximum 100 characters)
	Initial density (Real)
	Reference density used in E.O.S (equation of state) Default = (Real)
Ireac	Ignition and growth model flag. (Integer) = 1: for Lee-Tarver (default) = 2: for Dyna
Ar	Reagents JWL parameter (Real)
Br	Reagents JWL parameter (Real)
	Reagents JWL parameter (Real)
	Reagents JWL parameter (Real)
	Reagents JWL parameter (Comment 4) (Real)
AP	Product JWL parameter (Real)
BP	Product JWL parameter (Real)
	Product JWL parameter (Real)
	Product JWL parameter (Real)
	Product JWL parameter (Real)
	Heat capacity reagents (Real)
	Heat capacity product (Real)
EQ	Heat reaction (Real)
itr	Maximum number of iterations for the mixing law Default = 80 (Integer)
	Precision on hydrodynamic balance Default = 10-3 (Real)
check	Limiter of the mass fraction of products Default = 10-5 (Real)
rki	Chemical kinetic coefficient of the starting phase (Lee-Tarver and Dyna-2D) (Real)
ex	Chemical kinetic coefficient of the starting phase (Lee-Tarver and Dyna-2D) (Real)
ri	Chemical kinetic coefficient of the starting phase (Lee-Tarver and Dyna-2D) (Real)
rkg	Chemical kinetic coefficient of the growing phase (Lee-Tarver and Dyna-2D) (Real)
yg	Chemical kinetic coefficient of the growing phase (Lee-Tarver and Dyna-2D) (Real)
zg	Chemical kinetic coefficient of the growing phase (Lee-Tarver and Dyna-2D) (Real)
ex1	Chemical kinetic coefficient of the growing phase (Dyna-2D) (Real)
k	Numerical limiters coefficient (Lee-Tarver and Dyna-2D) Default = 99.0 (Real)
X	Numerical limiters coefficient (Dyna-2D) Default = 99.0 (Real)
tol	Numerical limiters coefficient (Dyna-2D) Default = 0.0 (Real)
grow2	Growing phase 2 coefficient (Dyna-2D) (Real)
ex2	Growing phase 2 coefficient (Dyna-2D) (Real)
yg2	Growing phase 2 coefficient (Dyna-2D) (Real)
zg2	Growing phase 2 coefficient (Dyna-2D) (Real)
ccrit	Starting threshold (for compression) (Dyna-2D) (Real)
fmxig	Starting threshold (mass fraction) (Dyna-2D) (Real)
fmxgr	Coefficient (Dyna-2D) (Comment 5) (Real)
fmngr	Coefficient (Dyna-2D) (Comment 5) (Real)
G	Shear modulus (Real)
Ti	Initial temperature (K) (Real)

#RADIOSS STARTER

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

#- 2. MATERIALS:

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

/MAT/LAW41/1

LX17 (unit Mg-mm-s)

# RHO_I RHO_0

1900 0

# Ireac

# Ar Br R1r R2r R3r

4930000000000 -166000000000 7.44 3.72 3.3337E-5

# Ap Bp R1p R2p R3p

696000000000 2500000000 4.4 .94 4.3E-6

# Cvr Cvp Eq

2781 1000 .088

# iter EPS check

0 0 0

# rki ex ri

100000000 1 4

# rkg yg zg ex1

1000000000 .371 3 .191

# K X tol

0 0 0

# grow2 ex2 yg2 zg2

0 1 1 1

# ccrit fmxig fmxgr fmngr

0 .25 1 100

# G Ti

75000000 298

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

#ENDDATA

/END

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

1.	If f is the mass fraction of the products and p is the reduced pressure:

Ireact = 1: “Ignition and growth” according to Lee/Tarver

mat_law41_Ireac1

Ireac = 2: “Ignition and growth” according to the formulation introduced in Dyna-2D

mat_law41_Ireac2

2.	Coefficient grow1 is initialized by rkg

3.	Coefficients yg1 and zg1 are respectively initialized by yg and zg.

4.	Coefficients R3 and are linked by the relation: R3 = Cv

5.	Coefficients fmxgr and fmngr are the limiters of the growth rate according to the mass fraction of products.

6.	This material law is not compatible with ALE.

7.	Heat reaction energy EQ is supposed to be constant.

8.	Reagent pressure Pr and detonation products pressure Pr are computed using a modified Jones-Wilkins-Lee equation of state:

In term of relative volume :

Where, , R3 = Cv

In terms of :

Where,

, and R3 = Cp

E.L. Lee and C.M. Tarver "Phenomenological model of shock initiation in heterogeneous explosives" Phy. Fluids Vol. 23, No. 12, December 1980.

/MAT/LAW41 (LEE-TARVER)

/MAT/LAW41 (LEE-TARVER)

/MAT/LAW41 (LEE-TARVER)

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