# Numerical and Experimental Studies of the LK Type Shaped Charge
## 6 Conclusions  
This article presents the results of modeling the cumulative jet for the LK charge. The SPH method enabled us to obtain accurate results from modeling cumulative core formation with a relatively fast calculation time. The results from the numerical simulation (see Figure 13) of the jet velocity showed a correlation with the results described in the literature. As indicated, the jet front reaches speeds between 7 and 10 km/s (see Figure 1). In the case of numerical simulation, a speed is included in this range. It has been shown that the modification of the LK charge had a positive effect on jet amplification, with an inevitable collapse in the final stage of formation (see Figure 14). This is also due to the increased initiation of the cumulative jet's velocity, which indicated better parameters for the peripheral charge. The above was also confirmed in the experiment. Numerical tests and theoretical analysis (see Section 2) show that the jet still retains its ability to penetrate after penetrating the shield. It follows that this LK charge can effectively pierce shields of this type with a thickness of more than three calibers. It has been observed that peripherally initiated charges have a positive effect on the jet  
Figure 17: Simulations of cumulative charges with liners of different material structures: (**a**) formation of the cumulative jet; (**b**) jet velocities for different insert materials.  
growth in the process of the collapsing liner. Moreover, it was confirmed with the literature data that the material for the liner is of significant importance in achieving the velocity of the cumulative jet (see Figure 17). Summarizing the presented results of modeling the efficiency of the jet, based on numerical methods applied to the LK-shaped charge, confirms the correct direction of the research. The results presented, which are mostly based on simulation studies, will be validated in multi-variant ballistic tests, as well as in the material examination of the liner in further work.  
Conceptualization, K.J., A.K. and D.P.; methodology, K.J., A.K., M.B. ([PERSON]) and M.B. ([PERSON]); software, D.P., M.B. ([PERSON]) and M.M.; validation, M.B. ([PERSON]) and D.P.; formal analysis, A.K., K.J., M.B. ([PERSON]), D.P. and J.S.; investigation, K.J., J.S. and D.P.; resources, K.J., M.B. ([PERSON]) and M.M.; data curation, A.K., K.J., D.P. and M.B. ([PERSON]); writing--original draft preparation, K.J., D.P. and A.K.; writing--review and editing, M.M., M.B. ([PERSON]) and M.B. ([PERSON]); visualization, A.K., K.J., J.S. and D.P.; supervision, K.J., M.B. ([PERSON]) and M.M.; project administration, D.P., A.K. and M.B. ([PERSON]); funding acquisition, M.B. ([PERSON]), K.J. and M.M. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Centre for Research and Development of Poland, grant No. TECHMATSTRATEG 2/410049/12/NCBR/2019. Calculations have been carried out in Wroclaw Centre for Networking and Supercomputing ([[http://www.wcss.pl](http://www.wcss.pl)]([http://www.wcss.pl](http://www.wcss.pl))), grant No. 452.  
The authors declare no conflict of interest.