Iform = 10
Block Format Keyword Able to handle up to four materials: Three elasto-plastic materials (solid, liquid, or gas), and one high explosive material (JWL EOS).
The material law is based on a diffusive interface technique. For sharper interfaces between submaterial zone, refer to /ALE/MUSCL.
It is not recommended to use this law with Radioss single precision engine.
- P
- Positive for a compression and negative for traction.
Where, mean that the EOS is linear for an expansion and cubic for a compression.
By default, the process is adiabatic . To enable thermal computation, refer to 6.
Where, V is relative volume: and is the internal energy per unit initial volume: . 9 to 13
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW51/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
Blank | |||||||||
Iform |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
Pext |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
amat_1 | bmat_1 | nmat_1 | |||||||
cmat_1 | |||||||||
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
A | B | R1 | R2 | ||||||
D | PCJ | IBFRAC |
Definitions
Field | Contents | SI Unit Example |
---|---|---|
mat_ID | Material
identifier. (Integer, maximum 10 digits) |
|
unit_ID | Unit Identifier (Integer, maximum 10 digits) |
|
mat_title | Material
title. (Character, maximum 100 characters) |
|
Iform | Formulation
flag. (Integer) |
|
Pext | External pressure. 2 Default = 0 (Real) |
|
Kinematic viscosity shear
. 3 Default = 0 (Real) |
||
Kinematic viscosity
(volumetric),
which corresponds to Stokes
Hypothesis. 3 Default = 0 (Real) |
||
Initial volumetric
fraction. 4 (Real) |
||
Initial
density. (Real) |
||
Initial energy per unit
volume. (Real) |
||
Hydrodynamic cavitation
pressure. 5 If fluid material ( ), then default = -Pext If solid material ( ), then default = -1e30. (Real) |
||
Initial
pressure. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic coefficient.
9 (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Elasticity shear modulus.
(Real) |
||
Plasticity yield
stress. (Real) |
||
Plasticity hardening
parameter. (Real) |
||
Plasticity hardening
exponent. Default = 1.0 (Real) |
||
Strain rate coefficient.
Default = 0.00 (Real) |
||
Reference strain
rate. If , no strain rate effect (Real) |
||
Temperature
exponent. Default = 1.00 (Real) |
||
Initial
temperature. Default = 300 K (Real) |
||
Melting temperature.
Default = 1030 (Real) |
||
Maximum
temperature. Default = 1030 (Real) |
||
Specific heat per unit of
volume. 7 (Real) |
||
Failure plastic
strain. Default = 1030 (Real) |
||
Plasticity maximum
stress. Default = 1030 (Real) |
||
Thermal conductivity
coefficient 1. 8 (Real) |
||
Thermal conductivity
coefficient 2. 8 (Real) |
||
Initial volumetric
fraction of unreacted explosive. 4 (Real) |
||
Initial density of
unreacted. explosive (Real) |
||
Detonation
energy. (Real) |
||
Minimum pressure. 5 Default = (Real) |
||
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) |
|
Hydrodynamic coefficient
for unreacted explosive. 9 (Real) |
||
IBFRAC | Burn Fraction Calculation
flag. 11
(Integer) |
Example
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW51/99
99.99% Water + 0.01% Air-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
# IFORM
10
#---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
0.0001 1.2 2.5E+05 0 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
0.9999 1000.0 0 0 1E+5
# C_1_2 C_2_2 C_3_2 C_4_2 C_5_2
2.25E+9 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 Plastic material with Johnson-Cook Yield criteria-----------------------#
# 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 1.0E+05
# B_1 B_2 R_1 R_2 W
371.20E+9 3.231E+9 4.15 0.9499 0.3
# D P_CJ C_14 I_BFRAC
6930.0 2.1E+10 22.5E+5 0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
Comments
- Numerical diffusion can be improved using the second order method for volume fraction convection, /ALE/MUSCL. The previous /UPWIND used to limit diffusion is now obsolete.
-
Radioss computes and outputs a relative pressure
.
(7) However, total pressure is essential for energy integration ( ). It can be computed with the external pressure flag Pext.
leads to .
This means if Pext = 0, the computed pressure is also the total pressure .
- Kinematic
viscosities are global and is not specific to each material. It allows computing
viscous stress tensor:
(8) Where,- Kinematic shear viscosity flag
- Kinematic volumetric viscosity flag
- 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.
-
flag is the minimum value for the computed
pressure
. It means that total pressure is also bounded
to:
(9) For fluid materials and detonation products, must remain positive to avoid any tensile strength so must be set to .
For solid materials, default value = 1e-30 is suitable but may be modified.
- By default, the
process is adiabatic:
. 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:
(10) For solids and liquids, for perfect gas:
- The temperature evolution in the Johnson-Cook model is computed with the flag , even if the thermal card (/HEAT/MAT) is not defined.
- Thermal
conductivity,
, is linearly dependent on the
temperature:
(11) -
can be estimated 1 with
(12) Where, is the speed of sound in the unreacted explosive and an estimation for TNT is 2000 m/s.
- Explosive material ignition is made with detonator cards, /DFS/DETPOINT or /DFS/DETPLAN.
- 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: .
A detonation time Tdet is computed by the Starter from the detonation velocity. During the simulation the burn fraction is computed as:(13) Where, the burn fraction calculation from burning time is:(14) and the burn fraction calculation from volumetric compression is:(15) 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:
IBFRAC = 2:
- 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
whose first value is detonation time (with
opposite sign) and positive values corresponds to the burn fraction
evolution.
(16) - Detonation times can be written in the Starter output file for each JWL element. The printout flag (Ipri) must be greater than or equal to 3 (/IOFLAG).
- Material tracking
is possible through animation files:
/ANIM/BRICK/VFRAC (volumetric fractions for all materials)