Iform = 10

Block Format Keyword

/MAT/LAW51 - Iform = 10: Multi-material Law with up to 3 Elasto-plastic Materials (Solid, Liquid, or Gas) and one high explosive

Description

Able to handle up to four materials:

•	Three elasto-plastic materials (solid, liquid, or gas)

•	One high explosive material (JWL EOS).

The material boundaries inside an element are not explicitly defined, but an anti-diffusive technique is used to avoid expansion of transition zone (Comment 1).

Compatible only with 3D analysis and Euler or ALE formulation.

LAW51 is based on equilibrium between each material present inside the element. RADIOSS computes and outputs a relative pressure . At each cycle:

= 1 = 2 = 3= 4

Total pressure can be calculated with external pressure:

P = + Pext.

Where, P is positive for a compression and negative for traction.

Hydrostatic stresses are computed from Polynomial EOS:

Where, which means that the EOS is linear for an expansion and cubic for a compression.

By default, the process is adiabatic Q = 0. To enable thermal computation, refer to Comment 6.

Deviatoric stresses are computed with a Johnson-Cook model:

High explosive material is modeled with linear EOS if unreacted and JWL EOS for detonation products:

Where, V is relative volume: V = Volume / V0 and E is the internal energy per unit initial volume: E = Eint / V0. For more details, refer to Comments 9 to 13.

Format

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
/MAT/LAW51/mat_ID
mat_title
Blank
Iform

#Global Parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
Pext

#Material1 Parameters

(1)	(3)	(5)	(7)	(9)
		E0mat_1		C0mat_1
C1mat_1	C2mat_1	C3mat_1	C4mat_1	C5mat_1
G1mat_1	amat_1	bmat_1	nmat_1
cmat_1	mat_1
mmat_1	T0mat_1	Tmeltmat_1	Tlimmat_1
		KAmat_1	KBmat_1

#Material2 Parameters

(1)	(3)	(5)	(7)	(9)
		E0mat_2		C0mat_2
C1mat_2	C2mat_2	C3mat_2	C4mat_2	C5mat_2
G1mat_2	amat_2	bmat_2	nmat_2
cmat_2	mat_2
mmat_2	T0mat_2	Tmeltmat_2	Tlimmat_2
		KAmat_2	KBmat_2

#Material3 Parameters

(1)	(3)	(5)	(7)	(9)
		E0mat_3		C0mat_3
C1mat_3	C2mat_3	C3mat_3	C4mat_3	C5mat_3
G1mat_3	amat_3	bmat_3	nmat_3
cmat_3	mat_3
mmat_3	T0mat_3	Tmeltmat_3	Tlimmat_3
		KAmat_3	KBmat_3

#Material4 Parameters (Explosive)

(1)	(3)	(5)	(7)	(9)
		E0mat_4		C0mat_4
A	B	R1	R2
D	PCJ	C1mat_4		IBFRAC

Field	Contents	SI Unit Example
mat_ID	Material identifier (Integer, maximum 10 digits)
mat_title	Material title (Character, maximum 100 characters)
Iform	Formulation flag (Integer)
Pext	External pressure (Comment 2) Default = 0 (Real)
	Kinematic viscosity shear (Comment 3) Default = 0 (Real)
	Kinematic viscosity (volumetric), which corresponds to Stokes Hypothesis (Comment 3) Default = 0 (Real)
	Initial volumetric fraction (Comment 4) (Real)
	Initial density (Real)
E0mat_i	Initial energy per unit volume (Real)
	Hydrodynamic cavitation pressure (Comment 5) If fluid material (), then default = -Pext If solid material (), then default = -1e30 (Real)
C0mat_i	Initial pressure (Real)
C1mat_i	Hydrodynamic coefficient (Real)
C2mat_i	Hydrodynamic coefficient (Real)
C3mat_i	Hydrodynamic coefficient (Real)
C4mat_i	Hydrodynamic coefficient (Real)
C5mat_i	Hydrodynamic coefficient (Real)
G1mat_i	Elasticity shear modulus Default = 0 (Fluid material) (Real)
amat_i	Plasticity yield stress (Real)
bmat_i	Plasticity hardening parameter (Real)
nmat_i	Plasticity hardening exponent Default = 1.0 (Real)
cmat_i	Strain rate coefficient Default = 0.00 (Real) = 0: no strain rate effect
mat_i	Reference strain rate (Real) If no strain rate effect
mmat_i	Temperature exponent Default = 1.00 (Real)
T0mat_i	Initial temperature Default = 300 K (Real)
Tmeltmat_i	Melting temperature Default = 1030 (Real) = 0: no temperature effect
Tlimmat_i	Maximum temperature Default = 1030 (Real)
	Specific heat per unit of volume (Comment 7) (Real)
	Failure plastic strain Default = 1030 (Real)
	Plasticity maximum stress Default = 1030 (Real)
KAmat_i	Thermal conductivity coefficient 1 (Comment 8) (Real)
KBmat_i	Thermal conductivity coefficient 2 (Comment 8) (Real)
	Initial volumetric fraction of unreacted explosive (Comment 4) (Real)
	Initial density of unreacted explosive (Real)
E0mat_4	Detonation energy (Real)
	Minimum pressure (Comment 5) Default = -Pext (Real)
C0mat_4	Initial pressure of unreacted explosive (Real)
A	JWL EOS coefficient (Real)
B	JWL EOS coefficient (Real)
R1	JWL EOS coefficient (Real)
R2	JWL EOS coefficient (Real)
	JWL EOS coefficient (Real)
D	Detonation velocity
PCJ	Chapman-Jouget pressure (Real)
C1mat_4	Hydrodynamic coefficient for unreacted explosive (Comment 8) (Real)
IBFRAC	Burn Fraction Calculation flag (Comment 11) (Integer) = 0: Volumetric Compression + Burning Time = 1: Volumetric Compression only = 2: Burning Time only

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

/MAT/LAW51/99

time0:100%Water - MULTIMAT:AIR+WATER+TNT,units {kg,m,s,Pa}

#(output is total pressure:Pext=0)

#--------------------------------------------------------------------------------------------------#

# Material Law No 51. MULTI-MATERIAL SOLID LIQUID GAS -ALE-CFD-SPH

#--------------------------------------------------------------------------------------------------#

# Blank format

# IFLG

#---Global parameters------------------------------------------------------------------------------#

# P_EXT NU LAMDA

0 0 0

#---Material#1:AIR(PerfectGas)---------------------------------------------------------------------#

# ALPHA_1 RHO_0_1 E_0_1 P_MIN_1 C_0_1

0.0 1.2 2.5E+05 -1E30 0

# C_1_1 C_2_1 C_3_1 C_4_1 C_5_1

0 0 0 0.4 0.4

# G_1 SIGMA_Y_1 BB_1 N_1

0 0 0 0

# CC_1 EPSILON_DOT_0_1

0 0

# CM_1 T_10 T_1MELT T_1LIMIT RHOCV_1

0 0 0 0 0

# EPSILON_MAX_1 SIGMA_MAX_1 K_A_1 K_B_1

0 0 0 0

#---Material#2:WATER(Linear_Incompressible)--------------------------------------------------------#

# ALPHA_2 RHO_0_2 E_0_2 P_MIN_2 C_0_2

1.0 1000.0 2.5E+05 -1E30 1E+5

# C_1_2 C_2_2 C_3_2 C_4_2 C_5_2

0 0 0 0 0

# G_2 SIGMA_Y_2 BB_2 N_2

0 0 0 0

# CC_2 EPSILON_DOT_0_2

0 0

# CM_2 T_20 T_2MELT T_2LIMIT RHOCV_2

0 0 0 0 0

# EPSILON_MAX_2 SIGMA_MAX_2 K_A_2 K_B_2

0 0 0 0

#---Material#3:not defined-------------------------------------------------------------------------#

# ALPHA_3 RHO_0_3 E_0_3 P_MIN_3 C_0_3

0.0 0 0 0 0

# C_1_3 C_2_3 C_3_3 C_4_3 C_5_3

0 0 0 0 0

# G_3 SIGMA_Y_3 BB_3 N_3

0 0 0 0

# CC_3 EPSILON_DOT_0_3

0 0

# CM_3 T_30 T_3MELT T_3LIMIT RHOCV_3

0 0 0 0 0

# EPSILON_MAX_3 SIGMA_MAX_3 K_A_3 K_B_3

0 0 0 0

#---Material#4:TNT(JWL)----------------------------------------------------------------------------#

# ALPHA_4 RHO_0_4 E_0_4 P_MIN_4 C_0_4

0.0 1590 7.0E+9 1E-30 1E+5

# B_1 B_2 R_1 R_2 W

371.20E+9 3.231E+9 4.15 0.95 0.3

# D P_CJ C_14 I_BFRAC

6930.0 21.0E+9 22.5E+5 0

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

1.	The anti-diffusive technique can be adjusted with /UPWIND from Starter Input. The 3 flag is the upwind coefficient for a damp area:

3 = 1: Full Upwind (default, recommended value)

3 = 1e-30: Zero Upwind (less diffusive, but potentially unstable)

3 = -1: Full Downwind (Anti-Diffusive technique, potentially unstable)

2.	RADIOSS computes and outputs a relative pressure .

However, total pressure is essential for energy integration (dEint = -PdV). It can be computed with the external pressure flag Pext.

P = + Pext leads to dEint = -(Pext + ) dV.

This means if Pext = 0, the computed pressure is also the total pressure = P.

3.	Kinematic viscosities are global and is not specific to each material. It allows computing viscous stress tensor:

Where, is the cinematic shear viscosity flag, and

is the cinematic volumetric viscosity flag.

4.	Volumetric fractions enable the sharing of elementary volume within the three different materials.

For each material must be defined between 0 and 1.

Sum of initial volumetric fractions must be equal to 1.

For automatic initial fraction of the volume, refer to the /INIVOL card.

5.	flag is the minimum value for the computed pressure . It means that total pressure is also bounded to:

For fluid materials and detonation products must remain positive to avoid any tensile strength so must be set to -Pext.

For solid materials, default value = -1e30 is suitable but may be modified.

6.	By default, the process is adiabatic: Q = 0. Heat contribution is computed only if the thermal card is associated to the material law (/HEAT/MAT).

In this case and the parameters for thermal diffusion are read for each material:

For solids and liquids,, and for perfect gas .

7.	The temperature evolution in the Johnson-Cook model is computed with the flag , even if the thermal card (/HEAT/MAT) is not defined.

8.	Thermal conductivity, K, is linearly dependent on the temperature:

K(T) = KA + KBT

9.	It is highly recommended to provide a strictly positive coefficient for unreacted explosive EOS in order to ensure equilibrium calculation and numerical stability.

If this value is unknown, a stable and acceptable value is:

Where, is the clarity of the sound in water (SI:1500m/s).

10.	Explosive material ignition is made with detonator cards, /DFS/DETPOIN or /DFS/DETPLAN.

11.	Detonation Velocity (D) and Chapman Jouget Pressure (PCJ ) are used to compute the burn fraction calculation (). It controls the release of detonation energy and corresponds to a factor which multiplies JWL pressure.

For a given time: P(V,E) = Bfrac Pjwl (V,E).

A detonation time Tdet is computed by the Starter from the detonation velocity. During the simulation the burn fraction is computed as follows:

Where,

is the burn fraction calculation from burning time.

is the burn fraction calculation from volumetric compression.

It can take several cycles for the burn fraction to reach its maximum value of 1.00.

Burn fraction calculation can be changed defining the IBFRAC flag:

IBFRAC = 1: $law5_Ibfrac1_eq$

IBFRAC = 2: $law5_Ibfrac2_eq$

12.	As of version 11.0.240, Time Histories for Detonation time and burn fraction are available through /TH/BRIC with BFRAC keyword. This allows to output a function f whose first value is detonation time (with opposite sign) and positive values corresponds to the burn fraction evolution.

dfs_detpoin_eq

13.	Detonation times can be written in the Starter listing file for each JWL element. The printout flag (Ipri) must be greater than or equal to 3 (/IOFLAG).

14.	Material tracking is possible through animation files:

/ANIM/BRICK/VFRAC (volumetric fractions for all materials)

15.	The following global outputs are available for animation files:

/ANIM/BRICK/PLA51 (global plasticity)

/ANIM/BRICK/TEM51 (global temperature)

/ANIM/BRICK/BF51 (high explosive burn fraction)