RD-E: 4602 Euler Formulation

The purpose of this example is to show how to simulate the cylinder expansion test and compare the simulation result to experimental data.

Detonation is initiated at the bottom of the explosive. Radial expansion of the cylinder is measured and compared to experimental data.

The following features are used in the model:

Multi-material
Euler property formulation with I_ale=2
Brick elements

Options and Keywords Used

Multi-Material Solid, Liquid, and Gas material law (/MAT/LAW51 (MULTIMAT))
Solid property (/PROP/TYPE14 (SOLID))
Boundary condition (/BCS)
Detonation plan (/DFS/DETPLAN)

Input Files

Before you begin, copy the file(s) used in this example to your working directory.

RD-E-4602_Euler.zip

Modeling Video

Model Description

A OFHC copper cylinder (1.53cm diameter, 0.26cm thickness, 30.5cm height) is filled with an explosive (TNT). Detonation is initiated at the bottom of the explosive. Radial expansion is measured at a length of 8*D cm. With an Euler formulation, the air has to be modeled to measure radial expansion.

Since this problem is axisymmetric, only a quarter of the cylinder is modeled.

Units: cm, $μ$ s, g, Mbar

Using the Multi-Material Solid, Liquid, and Gas material law (/MAT/LAW51), the copper cylinder material has the following characteristics using /MAT/HYD_JCOOK:

Material Properties

Value

Rho_Initial

8.96 (g/cm³)

Young's modulus

0.4229 (Pa)

Poisson coefficient

0.33

Yield stress

0.0009 (µBar)

Hardening parameter

0.00292 (µBar)

Hardening exponent

0.31

Strain rate coefficient

0.025

Reference strain rate

1e-06

Specific heat per volume

1e+20

EoS_Options_Input (Polynomial)

C0 1e-06 (µBar)
C1 = 1.38 (µBar)
C2 = 1.372 (µBar)

Radioss Card (Copper)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##HWCOLOR materials 10 4
/MAT/LAW51/10
LAW_51_Copper                                                                                       

#    Iform
        12
#                                     NU              Nu_Vol
                                                            
#    MatID           ALPHA_MAT
         1                 1.0
#    MatID           ALPHA_MAT
         1                 0.0
#    MatID           ALPHA_MAT
         3                 0.0
#    MatID           ALPHA_MAT
         2                 0.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Using Multi-Material Solid, Liquid, and Gas material law (/MAT/LAW51), the TNT material has the following characteristics using /MAT/LAW5 (JWL):

Material Properties: Value
Rho_initial: 1.63 (g/cm³)
A parameter EoS: 3.712 (µBar)
B parameter EoS: 0.0323 (µBar)
R1 parameter EoS: 4.15
R2 parameter EoS: 0.95
Omega parameter EoS: 0.3
Detonation velocity: 0.693
Chapman Jouguet pressure: 0.21 (µBar)
Detonation Energy per Unit Volume: 0.07
Initial pressure: 1e-06
Unreacted explosive bulk modulus: 0.036

Radioss Card (TNT)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##HWCOLOR materials 11 4
/MAT/LAW51/11
LAW_51_TNT                                                                                          

#    Iform
        12
#                                     NU              Nu_Vol
                                                            
#    MatID           ALPHA_MAT
         1                 0.0
#    MatID           ALPHA_MAT
         1                 0.0
#    MatID           ALPHA_MAT
         3                 0.0
#    MatID           ALPHA_MAT
         2                 1.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Using the Multi-Material Solid, Liquid, and Gas material law (/MAT/LAW51), the Air material has the following characteristics using /MAT/HYD_VISC:

Material Properties

Value

Rho_Initial

0.0012 (g/cm³)

EoS_options_Input (IDEAL_GAS)

Heat Capacity Ratio = 1.4
Initial Pressure = 1e-06 (µBar)

Radioss Card (Air)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##HWCOLOR materials 12 4
/MAT/LAW51/12
LAW_51_Air                                                                                          

#    Iform
        12
#                                     NU              Nu_Vol
                                                            
#    MatID           ALPHA_MAT
         1                 0.0
#    MatID           ALPHA_MAT
         1                 0.0
#    MatID           ALPHA_MAT
         3                 1.0
#    MatID           ALPHA_MAT
         2                 0.0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Using the Multi-Material Solid, Liquid, and Gas material law (/MAT/LAW51), the Boundary material has the following characteristics.

Radioss Card (NRF)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
##HWCOLOR materials 4 6
/MAT/LAW51/4
NRF                                                                                                 

#    Iform
         6
#               Pext                           Tcp            Tc_alpha
                                                                      
#            ALPHA_1              RHO_01                E_01              P_min1                P_01
                 0.0                 0.0                 0.0                 0.0                 0.0
#             SSP_01
                 0.0
#    BLANK CARD

#            ALPHA_1              RHO_01                E_01              P_min1                P_01
                 0.0                 0.0                 0.0                 0.0                 0.0
#             SSP_01
                 0.0
#    BLANK CARD

#            ALPHA_1              RHO_01                E_01              P_min1                P_01
                 0.0                 0.0                 0.0                 0.0                 0.0
#             SSP_01
                 0.0
#    BLANK CARD

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

Model Method

A 3D mesh is made of brick elements. The element size for the copper cylinder is approximately 0.035 cm x 0.035 cm x 0.035 cm.

The mesh is dragged along the z direction (z = 30.5 cm). It is important to have no discontinuity in element volume to ensure a good propagation of detonation wave and shock wave.

Units: cm, $μ$ s, g, Mbar

The model is constraint in translational x-, y-, z- direction.

A planar detonation wave is defined at the bottom of the cylinder. A scale factor of 0.5 (on time step for all elements) is used for this type of application.

Property /PROP/SOLID with EULER property formulation Iale = 2 is used.

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#                q_a                 q_b                   h            LAMBDA_V                MU_V
#             dt_min   istrain      IHKT
##HWCOLOR properties 1 3
/PROP/SOLID/1
ALE_PROP                                                                                            
#   Isolid    Ismstr      Iale     Icpre  Itetra10     Inpts   Itetra4    Iframe                  Dn
         0         0         2                                        0                              
#                 qa                  qb                   h              Lambda                  Mu
                 1.1                0.05                                     0.0                 0.0
#         deltaT_min
                 0.0

Results

Figure 4 displays the variation of density and pressure in the cylinder, explosive and air. Energy balance is also displayed.

Figure 5 shows the comparison between the experimental and simulation measurement of radial expansion. The displacement values are estimated on the animations using the density contour.

Conclusion

Good correlation between experimental and simulation results. A thinner meshing could improve the correlation between simulation and experimental curves.

¹ Adiabatic Expansion of high explosive detonation products, LANL, Wilkins (1969)

² A Constitutive model and data for metals subjected to large strains, high strain rates and high temperatures, Gordon R. Johnson, William H. Cook