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ISSN 2744-1741 
Defense and Security Studies  Original Research 
Vol. 3, March 2022, pp.1-14 
https://doi.org/10.37868/dss.v3.id183 

This work is licensed under a Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/) that allows others 
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 1 

 
 
Numerical simulations of the formation behavior of explosively formed 
projectiles 
 
Minel Salkičević* 
1 Defense Technologies Department, Mechanical Engineering Faculty, University of Sarajevo 

* Corresponding author E-mail: s.minel97@gmail.com

Received Oct. 13, 2021 
Revised Dec. 22, 2021 
Accepted Jan. 12, 2022 

Abstract 
Explosively formed projectile (EFP) is a self-forging shape charged structure 
having very high penetration ability compared to conventional kinetic energy 
projectile. The penetration capability of an EFP is strongly dependent on various 
design parameters. The main parameters can be roughly divided into geometric 
and material parameters used in the warhead configuration.  
The present research is an effort to study the effect of metal casing thickness, type 
of metal used for casing, explosive type, liner thickness, type and configuration 
on the formation of EFP. Effectivness of an EFP is studied in terms of final 
velocity and shape of formed penetrator. The study is carried out by performing a 
number of simulations by using explicit finite element (FE) hydrocode 
ANSYS/Autodyn. 

© The Author 2022. 
Published by ARDA. 

Keywords: Explosively formed projectiles (EFP); Numerical Simulations; 
ANSYS/Autodyn  

1. Introduction 
Generally, an explosively formed projectile system consists of charge, liner, casing and wave-shaper. The 
geometric and physical parameters like length, diameter, liner shape and material and type of charge strongly 
influence the shape and velocity of the penetrator [1]. 

 
Figure 1. The schematic of EFP configuration [1] 



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Similar to shaped charge (cumulative) projectiles, after detonation, very high pressure collapses the liner into 
the appropriate shape (depending on the design) of the penetrator moving at a speed of up to 3 km/s [2].  
The process of penetrator formation from the initial shape of the liner is shown in Figure 2 [3]. 

 
Figure 2. The formation process of EFP [3] 

There are two structural types of solutions used in the fight against armored combat vehicles. The first type 
are anti-tank penetrating mines (with antenna or non-contact, electromagnetic activation mechanism), 
effective at a distance of up to one meter – one such is shown in Figure 3a. The second type are explosively 
formed projectiles that are used to pierce armor at greater distances (stand-off projectiles) – shown in Figure 
3b. The penetrating abilities of these two types are different, which results from the way of attacking the 
chosen target. The first type hits the floor plate or tracks of an armored vehicle (in modern tanks, the floor 
armor is not thicker than 20 mm). The second type hits the side armor (the thickness of the side armor in 
modern tanks does not exceed 80 mm), and in modern times also the upper side of the tank armor. The 
minimum penetrating power of the first type is 40 mm at a distance of up to one meter, and the second type - 
80 mm at a distance of up to 100 m [4]. 

 
Figure 3. Schematic representation of the solution based on the Misznay Schardin effect 

(a anti-tank mine; b-EFP; where: 1-liner, 2-exp. charge, 3- activation mechanism, 4-metal casing) [4] 

Two major applications have evolved since 1975 for EFP warheads, namely, long-standoff sensor-fuzed 
submunitions and medium-standoff, close-overflight missiles, as depicted in figure 4. The former application, 
which is the more traditional one, requires the formation of a single-piece EFP capable of flying in a stable 
position to the target. This refinement has led to the flared EFP rod and, more recently, to the finned EFP rod 
desings. For the medium – or short-standoff applications, a new type of EFP was developed. The need for an 
aerodynamic shape is not necessary for these applications because of the short distance the EFP must travel, 
hence, the length of the rod was increased and the flared tail was eliminated from the design. In fact, some of 
these rods are purposely stretched beyond their breaking point and fracture into several pieces resulting in 
greater total length [5]. 

INITIATION POINT 

EXPLOSIVE 
CHARGE 

LINER 

(1) INITIAL 
CONFIGURATION 

(2) FORMATION 
PROCESS 

(3) FINAL 
CONFIGURATION 



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Figure 4. Two modern applications of EFP technology [5] 

2. Numerical model 
The numerical model for simulations are generated using ANSYS/Autodyn software with appropriate 
boundary conditions and accurate geometric modeling. In order to predict behaviour of the liner, Euler grid is 
used to design all three components: the explosive, the liner and the casing geometry. The mesh is modelled 
using 0.25 mm rectangular cells in both regions (the jet formation and the transition region). The free space is 
filled with still air with an initial density of 0.001225 mg/mm3 and internal energy of 2.06640·105 micro-
Joules. Outflow boundary condition is applied to all computational borders except the symmetry. This allows 
the expanding detonation products to leave the computational domain without interacting with its boundaries. 
Figure 5. shows the initial geometry of standard EFP used in numerical simulations in this paper. [6] 
 

 
Figure 5. Geometry of simulated EFP [7] 

 
The initial geometry used in this investigation is shown in Fig.6. The HMX was used as exp. charge material. 
The shaped charge liner is made of copper with different forms and casing is made of steel. It is important to 
mention that the configurations and materials of previously mentioned parts varies with the test cases. [8] 



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Figure 6. EFP model used in the research (Autodyn) [8] 

3. Results and discussions 
In order to validate numerical model, a series of numerical simulations have been carried out. Obtained results 
were compared with numerical results found by Hussain et al, [7] where a good agreement was observed.  

3.1. Metal casing 
In this section, the influence of the metal casing wall thickness and the influence of the metal casing material 
will be analyzed. Initial configuration is shown in Figure 5. In order to show the influence of metal (steel 
4340) casing thickness on the process of penetrator formation, two numerical simulations were performed in 
the Autodyn software. The configuration of the EFP is the same in both simulations, only the thickness of the 
metal casing is varied. The thickness in the first simulation is 3 mm (Figure 7a). In the case of the second 
simulation, the thickness of the metal casing is 5 mm (Figure 7b). [8] 

 
 

Figure 7. Different metal casing thicknesses used in numerical simulations (Solidworks) [8] 

Figure 8 shows formed copper penetrators, as well as their velocities after 100 μs. It can be concluded that the 
thickness of the metal body affects the velocity of the formed penetrator - thicker casing corresponds to a 
higher velocity of the penetrator. In the case of the first simulation, the casing thickness was 3 mm and the 
penetrator velocity was about 1750 m/s (Figure 8 - left). In the second simulation, the casing thickness was 5 
mm, and the penetrator velocity was about 116 m/s higher than in the first simulation. The thicker the metal 
casing, around the explosive charge and the liner, the bigger the impact time of the explosive impulse and the 
bigger the total energy transmitted from the explosive to the liner. [8] 

Space 

Air 

Copper 

Steel 

HMX 

a) 

b) 



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Figure 8. Different penetrator velocities for different metal casing thicknesses (Autodyn) [8] 

Apart from the fact that body thickness has an influence on the process of penetrator formation in EFP, it is 
important to note that the body material also has a certain influence. So another simulation was done that 
shows the difference between the formed penetrators in the case of a steel casing and a casing made of 
aluminum. Namely, the geometry of the EFP from Figure 7a was used in the additional simulation. All the 
characteristics remained the same except that in the additional simulation, aluminum was used as the EFP 
casing material instead of steel (Figure 9). [8]  

 
Figure 9. Penetrator velocity of EFP with casing made of aluminum (Autodyn) [8] 

In Figure 9 it can be seen that the velocity of the penetrator, in the case of an aluminum casing, is about 1480 
m/s. If this velocity is compared to simulation in which the casing was made of steel, it can be concluded that 
in that case the penetrator had a higher velocity, by about 270 m/s. Material of higher density and higher 
values of yield strength increases the time of influence of the explosive impulse and increases the total energy 
transmitted from the explosive to the liner. [8]  
Table 1 shows the characteristics of the materials used (steel and aluminum), as well as the difference in 
penetrator velocities after 100 µs (t=100 µs). [8]  

Table 1. Characteristics of materials used for EFP’s casing and their influence on penetrator velocity [8] 

Casing material Density (kg/m3) 
Tensile strength 

(MPa) 
Yield strength 

(MPa) 
Penetrator velocity 

(m/s) 
Steel 7830 745 470 1750 

Aluminium 2700 305 215 1480 

It is also important to note that it is not always possible to choose a material with more favorable 
characteristics, due to limiting factors. Steel, as a material with higher density than aluminum, increases the 
overall system mass - which can be a limiting factor. [8] 

3.2. Explosive charge 
In this part, an analysis of the influence of explosive charge type on velocity of the formed penetrator will be 
performed, and a comparison will be made for the following three types of explosives: HMX, TNT and Comp 
B. In order to show the influence of the density and other characteristics of explosive charge on the process of 
penetrator formation, three more numerical simulations are presented below. Initial configuration shown in 
Figure 5 is retained (all measures, metal casing material – steel 4340, liner material – copper, metal casing 

Velocity (m/s) Velocity (m/s) 

Velocity (m/s) 



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thickness = 3 mm, liner thickness = 2 mm); however now the explosive charge is different (everything else is 
identical). Instead of the previously used HMX, now a TNT is used, with a lower density and therefore a 
lower detonation velocity (relative to HMX). [8] 
Figure 10 shows a penetrator, initiated by TNT, moving at a velocity of about 1380 m/s. Thus, the same EFP 
configuration with different explosive charge led to the conclusion that the penetrator velocity was higher by 
about 370 m/s in the case when octogen (HMX) was used as the explosive charge. [8] 
 

 
Figure 10. Penetrator velocity of EFP initiated by TNT, measured after 100 µs (Autodyn) [8] 

Figure 11 shows a penetrator, initiated by composition B, moving at a velocity of about 1635 m/s. The 
velocity of this penetrator is about 255 m/s higher than the penetrator initiated by TNT, and about 115 m/s 
lower than the velocity of the penetrator initiated by octogen.  
Table 2 compares the results for 3 EFP configurations with identical characteristics and different explosive 
charges. It can be easily seen from the table that a higher density of explosive guarantees a higher detonation 
velocity, and thus a higher value of the explosive impulse transmitted from the explosive to the liner. All 
previously mentioned penetrator velocities are measured after 100 µs from the initiation time point. [8] 

 

 
Figure 11. Penetrator velocity of EFP initiated by composition B, measured after 100 µs (Autodyn) [8] 

Table 2. Comparison of simulation parameters with different explosive charges [8] 

Simulation 
No. 

Exp. 
charge 

Charge density 
(kg/m3) 

Det. velocity 
(m/s) 

Penetrator 
velocity (m/s) 

Rel. diff. compared 
to TNT (%) 

1 HMX 1890 9110 1750 26.8 
2 TNT 1630 6940 1380 - 
3 Comp.B 1720 7620 1635 18.5 

 
Through the development of these projectiles, the charge with TNT itself was suppressed at the expense of 
more explosive mixtures with higher detonation velocities. This improvement leads to higher velocities and an 
increase in the slenderness of the penetrator, which increases its penetration capability. [8] 
 

Velocity (m/s) 

Velocity (m/s) 



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3.3. Metal liner 
In order to show the influence of the liner material on the penetrating capability of the EFP, a series of 
numerical simulations is presented below. The basic geometry of the EFP used in the simulations is shown in 
Figure 5.  
In this chapter the material of the liner will be varied - for the purpose of collecting information on the 
behavior of the explosive-formed penetrator depending on the liner material. Copper, aluminum, tantalum and 
iron will be used as the liner materials. After the material, the configuration and the thickness of the liner 
(made of copper) will also be analyzed. [8] 
The first material to be used in the simulation is aluminum, the characteristics of the aluminum used in the 
simulation are shown in Figure 12. [8] 
 

 
Figure 12. Characteristics of aluminum used in numerical simulation (Autodyn) [8] 

Aluminum is a material of relatively low density (2700 kg/m3); precisely because of its low density, the 
aluminum penetrator accelerates to high velocities (3500 m/s) in a short time interval. Figure 13 (left) shows 
the velocity of aluminum penetrator after 30 µs, and on the right after 50 µs. The velocity of the aluminum 
penetrator in both cases is about 3500 m/s. [8] 
In the figure on the right, it can be noticed that the penetrator is slowly tearing apart; the reason for that is the 
relatively low density of aluminum. This type of aluminum penetrator is not effective in the case of firing at 
targets located at a greater distance, unless the thickness of the liner is increased - in this case it is 2 mm, and 
it is constant. [8] 
 

 
 
Figure 13. Velocity and shape of aluminum made penetrator (Autodyn); left-after 30 µs, right-after 50 µs [8] 

Velocity (m/s) Velocity (m/s) 



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The other material to be used in the simulation is tantalum, the characteristics of the tantalum used in the 
simulation are shown in Figure 14. [8] 

 
Figure 14. Characteristics of tantalum used in numerical simulation (Autodyn) [8] 

Tantalum is a material of relatively high density (16690 kg/m3); because of its high density, tantalum 
penetrator hardly accelerates to high velocities, so that the penetrator remains at lower velocities during flight 
compared to other tested materials. [8] 
Figure 15 shows the velocity of tantalum penetrator after 100 µs. The velocity of the penetrator is around 
1125 m/s. The high density of tantalum guarantees that the penetrator barely loses its kinetic energy and is 
able to travel long distances. [8] 
 

 

 
Figure 15. Velocity and shape of tantalum made penetrator (Autodyn); after 100 µs [8] 

The third material that was used in the simulation is iron, and the main characteristics of iron used in the 
simulation are shown in Figure 16. [8] 
 

Velocity (m/s) 



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Figure 16. Characteristics of iron used in numerical simulation (Autodyn) [8] 

Iron, with a density about 7890 kg/m3, produces a penetrator with slightly higher velocity than the one made 
of copper. The velocity of the penetrator is around 1882 m/s (Figure 17), which is 132 m/s higher than for the 
copper penetrator. [8] 

 

 
Figure 17. Velocity and shape of iron made penetrator (Autodyn); after 100 µs [8] 

Penetrator velocities are presented in Table 3.  

Table 3. Comparison of penetrator velocities made of different materials [8] 

Liner material Time (µs) 
Penetrator velocity 

(m/s) 
Copper 100 1750 
Aluminium 50 3500 - detached part 
Aluminium 100 Penetrator tearing up
Tantalum 100 1125 
Iron 100 1882 

 

Velocity (m/s) 



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It can be noticed that there was a rupture of the aluminum penetrator; the detonation wave elongated 
aluminum penetrator way beyond its stretching limit - due to its low density and relatively weak atomic 
structure. The velocity and range of the tantalum penetrator are the smallest; this penetrator suffers the 
greatest decrease in density, which causes an increase in its temperature. Tantalum penetrator makes the 
largest hole (diameter) in the target (when breaking through the target, it results in a wider crater). The highest 
temperature occurs with tantalum penetrators - which also means the creation of hot fragments on the target. 
Due to its lower price, easy procurement and easy machining, iron is an attractive material for the production 
of EFP liners. The copper penetrator has the greatest slenderness - it is mostly used due to the greatest depth 
of penetration.  
Copper and mild steel are the main materials used to make the liners in the EFP configuration that provide the 
formation of a "solid" penetrator - Figure 18 (right). Tantalum, aluminum and iron are preferred in EFP 
configurations that guarantee the formation of a "hollow" penetrator - Figure 18 (left). [8] 

 
 

Figure 18. Hollow EF penetrator (left); Solid EF penetrator (right) [9] 

In addition to the liner material, the liner geometry itself has a great influence on the penetrator formation 
process. The various liner shapes and penetrators formed from such shapes will be shown below.  
The dependence between the geometry of the liner and the final shape of the penetrator is very complex and 
has not yet been adequately described. Numerical model that establishes a dependence between the finite 
velocity of the penetrator and the initial geometry of the liner is presented below. Two different models were 
used, the first model implies a constant liner thickness - the thickness in four configurations will vary from 5 
to 14% of the explosive charge diameter. The second model implies variable liner thickness (thickness 
increases or decreases from the periphery to the center of the liner) - as presented in Table 4. Copper will be 
used as the liner material, as an explosive charge HMX (octogen), and detonation will be performed from the 
point located at the rear end of the explosive charge - on the axis of symmetry. [8] 
For a constant liner thickness of 2 mm, a numerical simulation has already been presented earlier in the paper, 
the velocity of the penetrator was around 1750 m/s, and the mass of the liner was around 13 g. The kinetic 
energy of this penetrator is around 19.93 kJ, after 100 µs. [8] 
For a constant liner thickness of 3 mm, the liner mass is about 19.5 g and the penetrator velocity is around 
1305 m/s (Figure 19). The kinetic energy of this penetrator, after 100 µs is around 16.62 kJ. [8] 
 

 
Figure 19. Velocity and shape of copper made penetrator (Autodyn); after 100 µs (liner thickness = 3 mm) [8] 

Velocity (m/s) 



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For a constant liner thickness of 4 mm, the liner mass is around 26 g and the penetrator velocity is around 
1010 m/s (Figure 20). The kinetic energy of this penetrator is around 13.26 kJ. [8] 
 
 

 
Figure 20. Velocity and shape of copper made penetrator (Autodyn); after 100 µs (liner thickness = 4 mm) [8] 

For a variable liner thickness of 2 mm in the center, and 1 mm on the periphery, the liner mass is around 9.5 g 
and the penetrator velocity is around 1618 m/s (Figure 21). The kinetic energy of this penetrator is around 
12.45 kJ, after 100 µs. [8] 
 

 
Figure 21. Velocity and shape of copper made penetrator (Autodyn); after 100 µs – liner thickness is variable 

(2 mm – center; 1 mm – periphery) [8] 

For a variable liner thickness of 1 mm in the center and 2 mm on the periphery, the liner mass is around 9.36 g 
and the penetrator velocity after 20 µs is around 2900 m/s - the penetrator front end (Figure 22 - left). The 
kinetic energy of this penetrator is not relevant because it breaks.  
The figure 22 on the left shows the penetrator after 20 µs, while the figure on the right shows the penetrator 
after 30 µs. It is evident that due to the velocity gradient (the velocity of the penetrators front end is about 
2900 m/s and the velocity of the tail is about 1800 m/s) the penetrator will rupture - for these reasons the 
shaped charge jet is separated into primary and secondary jet (speaking of High-Explosive Anti-Tank 
warheads).  
In this case, the front end of the penetrator would have the greatest impact on the penetration of the projectile - 
the mass of the front part of the penetrator should be calculated in order to reach the actual value of kinetic 
energy, assuming that no subsequent rupture of the front end of the penetrator will take place. Penetration 
rupture occurs solely due to the difference (variation) between the velocities of the front end and tail of the 
penetrator (velocity gradient). [8] 
 
 

Velocity (m/s) 

Velocity (m/s) 



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Figure 22. Velocity and shape of copper made penetrator (Autodyn); after 100 µs – liner thickness is variable 

(1 mm – center; 2 mm – periphery) [8] 

In the specific case, the problem was the shape of the liner. The explosive impulse first reaches the part of the 
liner closest to it (the central part of the liner), accelerating the central, and in this case the thinnest part of the 
liner to a higher velocity than the peripheral parts. Numerical simulation showed that there will be a 
subsequent rupture of the penetrators front end, after approximately 65 µs, as shown in Figure 23. [8] 

 
Figure 23. Copper penetrator shape (Autodyn); after 65 µs - liner thickness is variable (1 mm center, 2 mm 

periphery) [8] 

Table 4 presents the results of simulations where the thickness of the liner was varied to describe the behavior 
of the penetrator - penetrator velocities were recorded after 100 µs, except for the velocity of 2900 m/s (after 
20 µs). [8] 

Table 4. Different geometries of EFP copper made liner [8] 

 
Figure 24 shows a fully formed copper made EF penetrator after 160 µs of simulation time. The thickness of 
the liner was in this case 2 mm. 
 

Velocity (m/s) Velocity (m/s) 

Liner 
configuration Thickness Liner mass (g) 

Penetrator 
velocity (m/s) 

Kinetic energy 
(kJ) 

Front end 



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Figure 24. Fully formed copper penetrator, after 160 µs (Autodyn) [8] 

4. Conclusions 
Based on theoretical considerations and analysis of available numerical model (presented in [7]) for predicting 
the shape, velocity, pressure distribution, density and kinetic energy of explosively formed penetrator, a 
numerical model was created in Autodyn (ANSYS) software.  
The data obtained from ref. [7] (all data obtained by numerical model presented in [7] is compared to the data 
obtained from experiment, and good agreement was achieved), and the data obtained by numerical simulation 
presented in this paper were compared. The following can be said: 

1. The penetrator velocities (provided with the model from [7]) have a satisfactory agreement with the 
penetrator velocities from numerical model presented in this paper. The largest difference between the 
values is 4.12%. Maximum deviations occur when the penetrator reaches a stable velocity (while the 
minimum deviations occur between 10 and 40 µs – depends on the liner material). 

2. The presented numerical model gives useful results, the values of the penetrator velocity and shape. 
Good agreement between the results of the numerical model and experiment data indicates that the 
initial and boundary conditions are well set. 

3. The advantage of the numerical model is that it allows the calculation of penetrators parameters based 
on varying the geometric, material and other characteristics of the liner, explosive and metal casing – 
performing relatively low-cost analysis. 

4. The accuracy of the numerical model depends on the mesh, initial and boundary conditions. The 
accuracy of the numerical model can be increased by modifying the mesh (i.e. by increasing the 
number of finite elements). 

 
Declaration of competing interest 
The authors declare that they have no any known financial or non-financial competing interests in any 
material discussed in this paper. 

Funding information 
No funding was received from any financial organization to conduct this research. 

 
 
 
 
 



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