# 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.

LAW51 is based on equilibrium between each material present inside the element. Radioss computes and outputs a relative pressure $\text{Δ}P$ . At each cycle:(1)
$\text{Δ}P=\text{Δ}P{\text{ }}_{1}=\text{Δ}P{\text{ }}_{2}=\text{Δ}P{}_{3}=\text{Δ}P{\text{ }}_{4}$
Total pressure can be calculated with external pressure:(2)
$P=\text{Δ}P+{P}_{ext}$
Where,
P
Positive for a compression and negative for traction.
Hydrostatic stresses are computed from Polynomial EOS:(3)
$-{\sigma }_{m}=\text{Δ}P={C}_{0}+{C}_{1}\mu +{C}_{2}^{\text{'}}{\mu }^{2}+{C}_{3}^{\text{'}}{\mu }^{3}+\left({C}_{4}+{C}_{5}\mu \right)E\left(\mu \right)$
(4)
$d{E}_{\mathrm{int}}=\delta W+\delta Q=-\left(\text{Δ}P+{P}_{ext}\right)dV+\text{​}\delta Q$

Where, $E={E}_{\mathrm{int}}/{V}_{0},\text{\hspace{0.17em}}{C}_{2}^{\text{'}}={C}_{2}{\delta }_{\mu \ge 0}\text{\hspace{0.17em}}and\text{\hspace{0.17em}}{C}_{3}^{\text{'}}={C}_{3}{\delta }_{\mu \ge 0}$ mean that the EOS is linear for an expansion and cubic for a compression.

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

Deviatoric stresses are computed with a Johnson-Cook model:(5)
${\sigma }_{dev}=\left\{\begin{array}{l}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }G\epsilon \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }if\text{\hspace{0.17em}}{\sigma }_{VM}\le \text{\hspace{0.17em}}\alpha \\ \left(\alpha +b{\epsilon }_{p}{}^{n}\right)\text{\hspace{0.17em}}\left(1+c\mathrm{ln}\frac{\stackrel{˙}{\epsilon }}{{\stackrel{˙}{\epsilon }}_{0}}\right)\text{\hspace{0.17em}}\text{\hspace{0.17em}}\left(1-{\left(\frac{T-{T}_{0}}{{T}_{melt}-{T}_{0}}\right)}^{m}\right)\text{ }if\text{\hspace{0.17em}}{\sigma }_{VM}>\text{\hspace{0.17em}}\alpha \end{array}$
High explosive material is modeled with linear EOS if unreacted and JWL EOS for detonation products:(6)
$\text{Δ}P=\left\{\begin{array}{l}\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{ }{C}_{0}+{C}_{1}\mu \text{ }\text{ }\text{ }\text{ }\text{ }\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{ }if\text{\hspace{0.17em}}T<\text{\hspace{0.17em}}{T}_{\mathrm{det}}\\ A\left(1-\frac{\omega }{{R}_{1}V}\right)\text{\hspace{0.17em}}{e}^{-{R}_{1}V}+B\left(1-\frac{\omega }{{R}_{2}V}\right){e}^{-{R}_{2}V}+\omega \frac{E}{V}\text{ }if\text{\hspace{0.17em}}{\sigma }_{VM}>\text{\hspace{0.17em}}\alpha \end{array}$

Where, V is relative volume: $V=Volume/{V}_{0}$ and $E$ is the internal energy per unit initial volume: $E={E}_{\mathrm{int}}/{V}_{0}$ . 9 to 13

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW51/mat_ID/unit_ID
mat_title
Blank
Iform
#Global Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Pext $\nu$ ${\nu }_{vol}$
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{mat\text{ }_\text{​}\text{ }1}$ ${\rho }_{0}^{mat\text{ }_\text{​}\text{ }1}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }1}$ $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_1\text{ }}$ ${C}_{0}^{mat\text{ }_\text{​}\text{ }1}$
${C}_{1}^{mat\text{ }_\text{​}\text{ }1}$ ${C}_{2}^{mat\text{ }_\text{​}\text{ }1}$ ${C}_{3}^{mat\text{ }_\text{​}\text{ }1}$ ${C}_{4}^{mat\text{ }_\text{​}\text{ }1}$ ${C}_{5}^{mat\text{ }_\text{​}\text{ }1}$
${G}_{1}^{mat\text{ }_\text{​}\text{ }1}$ amat_1 bmat_1 nmat_1
cmat_1 ${\stackrel{˙}{\epsilon }}_{0}^{mat\text{ }_\text{​}\text{ }1}$
${m}_{}^{mat\text{ }_\text{​}\text{ }1}$ ${T}_{0}^{mat\text{ }_\text{​}\text{ }1}$ ${T}_{melt}^{mat\text{ }_\text{​}\text{ }1}$ ${T}_{\mathrm{lim}}^{mat\text{ }_\text{​}\text{ }1}$ $\rho {C}_{v}^{mat\text{ }_\text{​}\text{ }1}$
${\epsilon }_{p,\mathrm{max}}^{mat\text{ }_1\text{ }}$ ${\sigma }_{\mathrm{max}}^{mat\text{ }_1}$ ${K}_{A}^{mat\text{ }_\text{​}\text{ }1}$ ${K}_{B}^{mat\text{ }_\text{​}\text{ }1}$
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{mat\text{ }_\text{​}\text{ }2}$ ${\rho }_{0}^{mat\text{ }_\text{​}\text{ }2}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }2}$ $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_2\text{ }}$ ${C}_{0}^{mat\text{ }_\text{​}\text{ }2}$
${C}_{1}^{mat\text{ }_\text{​}\text{ }2}$ ${C}_{2}^{mat\text{ }_\text{​}\text{ }2}$ ${C}_{3}^{mat\text{ }_\text{​}\text{ }2}$ ${C}_{4}^{mat\text{ }_\text{​}\text{ }2}$ ${C}_{5}^{mat\text{ }_\text{​}\text{ }2}$
${G}_{1}^{mat\text{ }_2}$ ${a}_{}^{mat\text{ }_\text{​}2}$ ${b}_{}^{mat\text{ }_\text{​}2}$ ${n}_{}^{mat\text{ }_\text{​}2}$
${c}_{}^{mat\text{ }_\text{​}2}$ ${\stackrel{˙}{\epsilon }}_{0}^{mat\text{ }_\text{​}2}$
${m}_{}^{mat\text{ }_2}$ ${T}_{0}^{mat\text{ }_2}$ ${T}_{melt}^{mat\text{ }_\text{​}\text{ }2}$ ${T}_{\mathrm{lim}}^{mat\text{ }_\text{​}\text{ }2}$ $\rho {C}_{v}^{mat\text{ }_\text{​}\text{ }2}$
${\epsilon }_{p,\mathrm{max}}^{mat\text{ }_\text{​}2\text{ }}$ ${\sigma }_{\mathrm{max}}^{mat\text{ }_2}$ ${K}_{A}^{mat\text{ }_2}$ ${K}_{B}^{mat\text{ }_2}$
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{mat\text{ }_\text{​}3}$ ${\rho }_{0}^{mat\text{ }_\text{​}3}$ ${E}_{0}^{mat\text{ }_\text{​}3}$ $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_\text{​}3\text{ }}$ ${C}_{0}^{mat\text{ }_\text{​}3}$
${C}_{1}^{mat\text{ }_\text{​}3}$ ${C}_{2}^{mat\text{ }_\text{​}3}$ ${C}_{3}^{mat\text{ }_\text{​}3}$ ${C}_{4}^{mat\text{ }_\text{​}3}$ ${C}_{5}^{mat\text{ }_\text{​}3}$
${G}_{1}^{mat\text{ }_\text{​}3}$ ${a}_{}^{mat\text{ }_\text{​}3}$ ${b}_{}^{mat\text{ }_\text{​}3}$ ${n}_{}^{mat\text{ }_\text{​}3}$
${c}_{}^{mat\text{ }_\text{​}3}$ ${\stackrel{˙}{\epsilon }}_{0}^{mat\text{ }_\text{​}3}$
${m}_{}^{mat\text{ }_\text{​}3}$ ${T}_{0}^{mat\text{ }_\text{​}3}$ ${T}_{melt}^{mat\text{ }_\text{​}3}$ ${T}_{\mathrm{lim}}^{mat\text{ }_\text{​}3}$ $\rho {C}_{v}^{mat\text{ }_\text{​}\text{ }\text{​}3}$
${\epsilon }_{p,\mathrm{max}}^{mat\text{ }_\text{​}3\text{ }}$ ${\sigma }_{\mathrm{max}}^{mat\text{ }_\text{​}3}$ ${K}_{A}^{mat\text{ }_\text{​}3}$ ${K}_{B}^{mat\text{ }_\text{​}3}$
#Material4 Parameters (Explosive)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{mat\text{ }_\text{​}\text{ }4}$ ${\rho }_{0}^{mat\text{ }_\text{​}\text{ }4}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }4}$ $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_\text{​}4\text{ }}$ ${C}_{0}^{mat\text{ }_\text{​}\text{ }4}$
A B R1 R2 $\omega$
D PCJ ${C}_{1}^{mat\text{ }_\text{​}\text{​}\text{ }4}$     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)

$\left[\text{Pa}\right]$
$\nu$ Kinematic viscosity shear $\nu =\mu /\rho$ . 3

Default = 0 (Real)

$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$
${\nu }_{vol}$ Kinematic viscosity (volumetric), ${\nu }_{vol}=\frac{3\lambda +2\mu }{\rho }$ which corresponds to Stokes Hypothesis. 3

Default = 0 (Real)

$\left[\frac{{\text{m}}^{\text{2}}}{\text{s}}\right]$
${\alpha }_{0}^{mat\text{ }_i}$ Initial volumetric fraction. 4

(Real)

${\rho }_{0}^{mat\text{ }_i}$ Initial density.

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
${E}_{0}^{mat\text{ }_i}$ Initial energy per unit volume.

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$
$\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_i\text{ }}$ Hydrodynamic cavitation pressure. 5

If fluid material ( ${G}_{1}^{mat\text{ }_i\text{ }}=0$ ), then default = -Pext

If solid material ( ${G}_{1}^{mat\text{ }_i\text{ }}\ne 0$ ), then default = -1e30.

(Real)

$\left[\text{Pa}\right]$
${C}_{0}^{mat\text{ }_i}$ Initial pressure.

(Real)

$\left[\text{Pa}\right]$
${C}_{1}^{mat\text{ }_i}$ Hydrodynamic coefficient.

(Real)

$\left[\text{Pa}\right]$
${C}_{2}^{mat\text{ }_i}$ Hydrodynamic coefficient.

(Real)

$\left[\text{Pa}\right]$
${C}_{3}^{mat\text{ }_i}$ Hydrodynamic coefficient.

(Real)

$\left[\text{Pa}\right]$
${C}_{4}^{mat\text{ }_i}$ Hydrodynamic coefficient. 9

(Real)

$\left[\text{Pa}\right]$
${C}_{5}^{mat\text{ }_i}$ Hydrodynamic coefficient.

(Real)

${G}_{1}^{mat\text{ }_i}$ Elasticity shear modulus.
= 0 (Default)
Fluid material

(Real)

$\left[\text{Pa}\right]$
${a}_{}^{mat\text{ }_i}$ Plasticity yield stress.

(Real)

$\left[\text{Pa}\right]$
${b}_{}^{mat\text{ }_\text{​}i}$ Plasticity hardening parameter.

(Real)

$\left[\text{Pa}\right]$
${n}_{}^{mat\text{ }_\text{​}i}$ Plasticity hardening exponent.

Default = 1.0 (Real)

${c}_{}^{mat\text{ }_\text{​}i}$ Strain rate coefficient.
= 0
No strain rate effect

Default = 0.00 (Real)

${\stackrel{˙}{\epsilon }}_{0}^{mat\text{ }_\text{​}i}$ Reference strain rate.

If $\stackrel{˙}{\epsilon }\le {\stackrel{˙}{\epsilon }}_{0}^{mat\text{​}_\text{​}i}$ , no strain rate effect

(Real)

$\left[\frac{\text{1}}{\text{s}}\right]$
${m}_{}^{mat\text{ }_\text{​}i}$ Temperature exponent.

Default = 1.00 (Real)

${T}_{0}^{mat\text{ }_i}$ Initial temperature.

Default = 300 K (Real)

$\left[\text{K}\right]$
${T}_{melt}^{mat\text{ }_i}$ Melting temperature.
= 0
No temperature effect

Default = 1030 (Real)

$\left[\text{K}\right]$
${T}_{\mathit{lim}}^{mat\text{ }_i}$ Maximum temperature.

Default = 1030 (Real)

$\left[\text{K}\right]$
$\rho {C}_{v}^{mat\text{ }_i}$ Specific heat per unit of volume. 7

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{3}\cdot \text{K}}\right]$
${\epsilon }_{p,\mathrm{max}}^{mat\text{ }_i\text{ }}$ Failure plastic strain.

Default = 1030 (Real)

${\sigma }_{\mathrm{max}}^{mat\text{ }_i\text{ }}$ Plasticity maximum stress.

Default = 1030 (Real)

$\left[\text{Pa}\right]$
${K}_{A}^{mat\text{ }_i}$ Thermal conductivity coefficient 1. 8

(Real)

$\left[\frac{\text{W}}{\text{m}\cdot \text{K}}\right]$
${K}_{B}^{mat\text{ }_i}$ Thermal conductivity coefficient 2. 8

(Real)

$\left[\frac{\text{W}}{\text{m}\cdot {\text{K}}^{2}}\right]$
${\alpha }_{0}^{mat\text{ }_4}$ Initial volumetric fraction of unreacted explosive. 4

(Real)

${\rho }_{0}^{mat\text{ }_4}$ Initial density of unreacted. explosive

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
${E}_{0}^{mat\text{ }_4}$ Detonation energy.

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$
$\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_4}$ Minimum pressure. 5

Default = $-{P}_{ext}$

(Real)

$\left[\text{Pa}\right]$
${C}_{0}^{mat\text{ }_4}$ Initial pressure of unreacted explosive.

(Real)

$\left[\text{Pa}\right]$
A JWL EOS coefficient.

(Real)

$\left[\text{Pa}\right]$
B JWL EOS coefficient.

(Real)

$\left[\text{Pa}\right]$
R1 JWL EOS coefficient.

(Real)

R2 JWL EOS coefficient.

(Real)

$\omega$ JWL EOS coefficient.

(Real)

D Detonation velocity. $\left[\frac{\text{m}}{\text{s}}\right]$
PCJ Chapman-Jouget pressure.

(Real)

$\left[\text{Pa}\right]$
${C}_{1}^{mat\text{ }_4}$ Hydrodynamic coefficient for unreacted explosive. 9

(Real)

$\left[\text{Pa}\right]$
IBFRAC Burn Fraction Calculation flag. 11
= 0
Volumetric Compression + Burning Time
= 1
Volumetric Compression only
= 2
Burning Time only

(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----|

1. 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.
2. Radioss computes and outputs a relative pressure $\text{Δ}P$ .(7)
$\text{Δ}P=\mathrm{max}\text{ }\left\{\text{Δ}P\text{​}\mathrm{min},\text{ }\text{\hspace{0.17em}}{C}_{0}+{C}_{1}\mu +{C}_{2}^{\text{'}}{\mu }^{2}+{C}_{3}^{\text{'}}{\mu }^{3}+\left({C}_{4}+{C}_{5}\mu \right)E\left(\mu \right)\right\}$

However, total pressure is essential for energy integration ( $d{E}_{\mathrm{int}}=-PdV$ ). It can be computed with the external pressure flag Pext.

$P=\text{Δ}P+{P}_{ext}$ leads to $d{E}_{\mathrm{int}}=-\left({P}_{ext}+\text{Δ}P\right)dV$ .

This means if Pext = 0, the computed pressure $\text{Δ}P$ is also the total pressure $\text{Δ}P=P$ .

3. Kinematic viscosities are global and is not specific to each material. It allows computing viscous stress tensor:(8)
$\tau =\mu \left[\left(\nabla \otimes V\right)+{\text{\hspace{0.17em}}}^{t}\text{​}\left(\nabla \otimes V\right)\right]+\lambda \left(\nabla V\right)I$
Where,
$\nu =\mu /\rho$
Kinematic shear viscosity flag
${\nu }_{vol}=\frac{3\left(\lambda +\frac{2\mu }{3}\right)}{\rho }$
Kinematic volumetric viscosity flag
4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

For each material ${\alpha }_{0}^{mat\text{ }_\text{​}\text{ }i}$ must be defined between 0 and 1.

Sum of initial volumetric fractions ${\sum }_{i=1}^{3}{\alpha }_{0}^{mat\text{​}_\text{​}i}$ must be equal to 1.

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

5. $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_i}$ flag is the minimum value for the computed pressure $\text{Δ}P$ . It means that total pressure is also bounded to:(9)
${P}_{\mathrm{min}}^{mat\text{ }_i}=\text{Δ}{P}_{\mathrm{min}}^{mat\text{​}_\text{​}i}+{P}_{ext}$

For fluid materials and detonation products, ${P}_{\mathrm{min}}^{mat\text{ }_i}$ must remain positive to avoid any tensile strength so $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_i}$ must be set to $-{P}_{ext}$ .

For solid materials, default value $\text{Δ}{P}_{\mathrm{min}}^{mat\text{ }_i}$ = 1e-30 is suitable but may be modified.

6. By default, the process is adiabatic: $\delta Q=0$ . Heat contribution is computed only if the thermal card is associated to the material law (/HEAT/MAT).
In this case, $\delta Q=\rho {C}_{V}VdT$ and the parameters for thermal diffusion are read for each material:(10)
$\rho {C}_{V}^{\mathit{mat}_i},{K}_{A}^{\mathit{mat}_i},{K}_{B}^{\mathit{mat}_i}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}{T}_{0}^{\mathit{mat}_i}$

For solids and liquids, ${C}_{\nu }\approx {C}_{p}$ for perfect gas: $\gamma ={C}_{p}/{C}_{\nu }$

7. The temperature evolution in the Johnson-Cook model is computed with the flag $\rho {C}_{V}^{\mathit{mat}_i}$ , even if the thermal card (/HEAT/MAT) is not defined.
8. Thermal conductivity, $K$ , is linearly dependent on the temperature:(11)
$K\left(T\right)={K}_{A}+{K}_{B}T$
9. can be estimated 1 with (12)

Where, ${c}_{0}^{unreacted}$ is the speed of sound in the unreacted explosive and an estimation for TNT is 2000 m/s.

10. Explosive material ignition is made with detonator cards, /DFS/DETPOINT or /DFS/DETPLAN.
11. Detonation Velocity (D) and Chapman Jouget Pressure (PCJ) are used to compute the burn fraction calculation ( ${B}_{frac}\in \left[0,1\right]$ ). It controls the release of detonation energy and corresponds to a factor which multiplies JWL pressure.

For a given time: $P\left(V,E\right)={B}_{frac}{P}_{jwl}\left(V,E\right)$ .

A detonation time Tdet is computed by the Starter from the detonation velocity. During the simulation the burn fraction is computed as:(13)
${B}_{frac}=\mathrm{min}\left(1,max\text{ }\left(\text{​}{B}_{f1},{B}_{f2}\right)\right)\text{​}$
Where, the burn fraction calculation from burning time is:(14)
and the burn fraction calculation from volumetric compression is:(15)
${B}_{f2}=\left\{\begin{array}{c}0,\begin{array}{c}\end{array}x<0\\ \frac{T-{T}_{det}}{1.5\text{Δ}x},\begin{array}{c}\end{array}x\ge 0\end{array}$

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: ${B}_{frac}=\text{min}\left(1,{B}_{f1}\right)$

IBFRAC = 2: ${B}_{frac}=\text{min}\left(1,{B}_{f2}\right)$

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.(16)
$\begin{array}{l}{T}_{\mathrm{det}}=-\mathrm{f}\left(0\right)\\ {B}_{frac}\left(t\right)=\left\{\begin{array}{l}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}0,\text{ }\text{\hspace{0.17em}}\text{\hspace{0.17em}}\mathrm{f}\left(t\right)<0\\ \mathrm{f}\left(t\right),\text{ }\mathrm{f}\left(t\right)\ge 0\end{array}\end{array}$
13. 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).
14. Material tracking is possible through animation files:

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

1 Hayes, B. "Fourth Symposium (International) on Detonation." Proceedings, Office of Naval Research, Department of the Navy, Washington, DC (1965): 595-601