10.6 Numerical Simulation
345
10.6.2.3 Air and Explosive
The linear polynomial Equation of State (EOS) is adopted to describe the air as
p = C 0 + C 1 μ + C 2 μ
2
+ C 3 μ
3
+ (C 4 + C 5 μ + C 6 μ
2
)E
(10.5)
where p is the pressure of the air, C 0 – C 6 are the user defined constants, E is the
internal energy per unit volume, μ = ρ/ρ 0 – 1, where ρ/ρ 0 is the ratio of current
density (ρ) to initial density (ρ 0 ). Since air can be assumed as an ideal gas, Eq. (10.5)
can be further simplified by setting C 0 = C 1 = C 2 = C 3 = C 6 = 0, and C 4 = C 5 =
γ – 1, where γ = 1.4 is the ratio of the specific heats for air. Hence, the pressure for
an idea gas can be expressed as
p = (γ − 1)
ρ
ρ 0
E
(10.6)
It should be noticed that the parameter of air density and E in Eq. (10.6) are
related to the temperature, that is, the different values for air density and specific
energy should be adopted according to specific local temperature.
The TNT explosive is described by Jones-Wikins-Lee (JWL) EOS as
p = A
1 −
ω
R 1 V
e
−R 1 V
+ B
1 −
ω
R 2 V
e
−R 2 V
+
ωE
V
(10.7)
where A, B, R 1 , R 2 , and ω are empirically derived constants which are different in
each explosive, V is the relative volume or the expansion of the explosive product,
and E is the detonation energy per initial unit volume. The parameters of the idea
gas and TNT explosive are given in Table 10.5.
10.6.3 Loading Scheme
Based on the present test, the UHPCC-FST column firstly endure the contact detonation and then the axial compressive load. Since the duration time of explosive
load is very short, while the axial compression test is a quasi-static process, if this
two processes are placed in a keyword file uninterruptedly, it will consume a lot of
computing resources. The restart input data method can divide the complete analysis
process into multiple stages. The analysis process can be interrupted at any time and
a restart file is simultaneously produced, in which the calculated results (damage,
volumetric strain and plastic deformation, etc.) at the terminal instant are stored. This
method can enhance the flexibility and controllability of the numerical analysis, as
well as reduce the elements number and improve the computation efficiency.
According to the modification degree of the original keyword file, the restart
input data method can be classified into three categories, i.e., simple restart, small
345
10.6.2.3 Air and Explosive
The linear polynomial Equation of State (EOS) is adopted to describe the air as
p = C 0 + C 1 μ + C 2 μ
2
+ C 3 μ
3
+ (C 4 + C 5 μ + C 6 μ
2
)E
(10.5)
where p is the pressure of the air, C 0 – C 6 are the user defined constants, E is the
internal energy per unit volume, μ = ρ/ρ 0 – 1, where ρ/ρ 0 is the ratio of current
density (ρ) to initial density (ρ 0 ). Since air can be assumed as an ideal gas, Eq. (10.5)
can be further simplified by setting C 0 = C 1 = C 2 = C 3 = C 6 = 0, and C 4 = C 5 =
γ – 1, where γ = 1.4 is the ratio of the specific heats for air. Hence, the pressure for
an idea gas can be expressed as
p = (γ − 1)
ρ
ρ 0
E
(10.6)
It should be noticed that the parameter of air density and E in Eq. (10.6) are
related to the temperature, that is, the different values for air density and specific
energy should be adopted according to specific local temperature.
The TNT explosive is described by Jones-Wikins-Lee (JWL) EOS as
p = A
1 −
ω
R 1 V
e
−R 1 V
+ B
1 −
ω
R 2 V
e
−R 2 V
+
ωE
V
(10.7)
where A, B, R 1 , R 2 , and ω are empirically derived constants which are different in
each explosive, V is the relative volume or the expansion of the explosive product,
and E is the detonation energy per initial unit volume. The parameters of the idea
gas and TNT explosive are given in Table 10.5.
10.6.3 Loading Scheme
Based on the present test, the UHPCC-FST column firstly endure the contact detonation and then the axial compressive load. Since the duration time of explosive
load is very short, while the axial compression test is a quasi-static process, if this
two processes are placed in a keyword file uninterruptedly, it will consume a lot of
computing resources. The restart input data method can divide the complete analysis
process into multiple stages. The analysis process can be interrupted at any time and
a restart file is simultaneously produced, in which the calculated results (damage,
volumetric strain and plastic deformation, etc.) at the terminal instant are stored. This
method can enhance the flexibility and controllability of the numerical analysis, as
well as reduce the elements number and improve the computation efficiency.
According to the modification degree of the original keyword file, the restart
input data method can be classified into three categories, i.e., simple restart, small