# Numerical and Experimental Studies of the LK Type Shaped Charge
## 1 Introduction  
The described cumulative effect was already being used for military applications during World War II in many varieties of anti-tank weapons. Technological developments after World War II took a rapid leap in terms of the advancement of cumulative missiles. The literature contains many studies of theoretical-experimental approaches to the problem [1; 2; 3; 4], whereby many parameters related to the cumulative effect have been analyzed. This phenomenon is very well described from the physical point of view [5; 6]. It should be noted that if a cone-shaped crater is hollowed out in a cylindrical explosive charge, its detonation will manifest a focusing of the explosive detonation products, generating intense local forces. This concentration of forces was used in the construction of shaped charges [6; 7]. The lining of this cavity with a specific material called a liner creates a jet which is driven by the wave emitted by the detonation of the explosive [8]. The jet formation process is caused by an increase in the pressure of detonation products acting on thelinear [9; 10]. The liner collapses under this pressure. The decomposition of the resultant pressure wave into orthogonal components, i.e. the radial component and the axial component, causes, on the one hand, causes the liner material to be compressed, while on the other hand driving the compressed material along the axis of symmetry of the operation of the very high pressure. The result of the collapse of the liner is the classic Birkhoff effect [11; 12], which results from the liner material in the slug and the jet (see Figure 1). As a consequence, this process leads to the creation of an appropriate and effective jet. This effect can be strengthened by the appropriate formation of the detonation wave front [12; 13]. This efficiency depends, among other things, on the type of insert material [6], its cone angle [14] and the speed of detonation wave front propagation (the so-called detonation velocity), \"i.e., it depends on the explosive material used [15; 16]\", and it usually amounts to 7-10 km/s. Studies have also been carried out with tandem heads, investigating their efficiency for armor [17; 18]. Among others, studies [19; 20; 21; 22] have analyzed various materials and thicknesses of cumulative inserts. The asymmetry of constructional parameters was examined in study [20], while the influences of the casing material, the linear angle, the spacing and many other parameters affecting the efficiency of the cumulative charge were comprehensively included in studies [23; 24; 25]. In [26], the focus was on bore-center annular-shaped charge studies, wherein the axial velocity and radial velocity of the head were analyzed. In study [27], inserts made of five different materials were compared. A truncated conical liner was compared with a classical conical-shaped charge. The truncated conical liner included a disc between the explosive material and the liner. In this way, the penetration depth was increased by several percent. The efficiency of single and double-layer liners was examined in [28] and compared with the penetration explosion effect of a single Cu liner. As the computational power of computers evolved, numerical methods applied to the advancement of science in relation to cumulative phenomenon also developed. Many mathematical-physical models have been created and employed in specialized software [29; 30], which can be adapted for research into, and the optimization and evaluation of, the parameters of various types of charges. Johnson-Cook (J-C) or Steinberg strength models have often been used [31; 32; 33] as they can accurately reproduce the formation of jets in metal materials. However, in the case of modern composite materials, the commonly used J-C strength model has limitations.