/MAT/LAW51 (Iform = 11) (Obsolete)
Block Format Keyword Able to handle up to four materials: Three elasto-plastic materials with polynomial EOS, following the available yield criteria: Johnson-Cook or Drucker-Prager, and one high explosive material with 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.
LAW51 is based on equilibrium between each material present inside the element. Radioss computes and outputs a relative pressure . At each cycle:
Total pressure can be calculated with external pressure:
- P
- Positive for a compression and negative for traction.
Hydrostatic stresses are computed from Polynomial EOS:
Where, mean that EOS is linear for an expansion and cubic for a compression.
By default, the process is adiabatic . To enable thermal computation, refer to 6.
Deviatoric stresses can be computed with either Johnson-Cook model or Drucker-Prager.
Johnson-Cook:
Drucker-Prager:
High explosive material is modeled with linear EOS if unreacted (for equilibrium purpose) and JWL EOS for detonation products:
Where, V is relative volume: and E is the internal energy per unit initial volume: . 9 to 12
Format
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
/MAT/LAW51/mat_ID/unit_ID | |||||||||
mat_title | |||||||||
Blank Format | |||||||||
Iform | Ipla_1 | Ipla_2 | Ipla_3 | ||||||
#Global parameters | |||||||||
Pext | v | ||||||||
#SubMaterial_1 parameters | |||||||||
(Input depends on Ipla_1 flag, see below) | |||||||||
#SubMaterial_2 parameters | |||||||||
(Input depends on Ipla_2 flag, see below) | |||||||||
#SubMaterial_3 parameters | |||||||||
(Input depends on Ipla_3 flag, see below) | |||||||||
#SubMaterial_4
parameters (Necessarily Jones-Wilkins-Lee material law) | |||||||||
A | B | R1 | R2 | ||||||
D | PCJ | IBFRAC |
Specific input for sub-material j (j= 1, 2, or 3) parameters.
amat_j | bmat_j | nmat_j | ||
cmat_j | ||||
mmat_j | ||||
Emat_j | vmat_j | |||
Definition
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) |
|
Ipla_j | Yield criteria flag
(sub-material index j could be 1, 2, or 3).
(Integer) |
|
#Global parameters | ||
Pext | External pressure.
2 Default = 0 (Real) |
|
v | Global Kinematic
viscosity (shear)
. 3 Default = 0 (Real) |
|
Global Kinematic
viscosity (volumetric)
. 3 Default = 0 (Real) (Stokes Hypothesis) |
||
#submaterial parameters for Polynomial EOS | ||
Initial volumetric
fraction. 4 (Real) |
||
Initial
density. (Real) |
||
Initial energy per
unit volume. (Real) |
||
Hydrodynamic
cavitation pressure. 5 Default = -10-30 (Real) |
||
Initial
pressure. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Hydrodynamic
coefficient. (Real) |
||
Elasticity shear
modulus. (Real) |
||
#submaterial parameters specific to Johnson-Cook yield criteria | ||
amat_j | Plasticity yield
stress. (Real) |
|
bmat_j | Plasticity
hardening parameter. (Real) |
|
nmat_j | Plasticity
hardening exponent. Default = 1.0 (Real) |
|
cmat_j | Strain rate coefficient.
Default = 0.00 (Real) |
|
Reference strain
rate. If means no strain rate effect (Real) |
||
mmat_j | Temperature exponent.
(Real) |
|
#submaterial parameters specific to thermal behavior | ||
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) |
||
#submaterial parameters specific to Drucker-Prager criteria | ||
Emat_j | Young's
modulus. (Real) |
|
vmat_j | Poisson's
ratio. (Real) |
|
Yield
coefficient. (Real) |
||
Yield
coefficient. (Real) |
||
Yield
coefficient. (Real) |
||
Yield
coefficient. (Real) |
||
#submaterial parameters specific to Jones-Wilkins-Lee EOS | ||
Initial volumetric
fraction of unreacted explosive. 4 (Real) |
||
Initial density of
unreacted explosive. (Real) |
||
Detonation
energy. (Real) |
||
Minimum pressure.
5 Default = -10-30 (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) |
|
Bulk modulus for
unreacted explosive. 9 (Real) |
||
IBFRAC | Burn fraction
calculation flag. 11
(Integer) |
Example
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW51/1
Underground explosion in Sand with Air,units{kg,m,s,Pa}
#---------------------------------------------------------------------------------------------------
# Material Law No 51. ALE MULTI-MATERIAL SOLID LIQUID GAS
#---------------------------------------------------------------------------------------------------
# IFORM IPLA_1 IPLA_2 IPLA_3
11 0 2 0
#---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 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
0
# T_10 T_1MELT T_1LIMIT RHOCV_1
0 0 0 0
# EPSILON_MAX_1 SIGMA_MAX_1 K_A_1 K_B_1
0 0 0 0
#---Material#2:SAND Plastic material with Drucker-Prager Yield Criteria----------------------------#
# ALPHA_2 RHO_0_2 E_0_2 P_MIN_2 C_0_2
1.0 1370 0 0 1.0E+05
# C_1_2 C_2_2 C_3_2 C_4_2 C_5_2
1.0E+09 2.5E+09 3.0E+10 0 0
# A0_2 A1_2 A2_2 A_MAX_2
0 0 0.25 0
# E_2 NU_2 B_MAT_2 MU_MAX_2
3.4E+09 0.3 0 0
# T_20 T_2MELT T_2LIMIT RHOCV_2
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 1638 7.0E+09 0 1.0E+05
# B_1 B_2 R_1 R_2 W
371199 3231 4.15 0.9499 0.3
# D P_CJ C_14 I_BFRAC
6930.0 2.1E+10 4.0E+09 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
.
However, total pressure is essential for energy integration ( ). It can be computed with the external pressure flag Pext.
leads to .
This means if , the computed pressure is also the total pressure .
- Kinematic
viscosities are global and not specific to each material for computing
viscous stress tensor:Where,
- Cinematic shear viscosity flag
- /
- Cinematic 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:
For fluid materials and detonation products, must remain positive to avoid any tensile strength so must be set to .
For solid materials, default value = -1e30 is suitable but may be modified.
- 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, 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, K, is linearly dependent on the
temperature:
-
can be estimated 1 with
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, refer to /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:
Where,
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:
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.
- 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).
- As of version 2023, this option is obsolete and should be replaced by Iform=12.