## 4 Problem Statement  
Our objective is to design a heterogeneous screen to protect critical spacecraft components from space debris particles. We aim to investigate the high-speed interaction between spherical space debris particles and protective screens made of various structures using specified materials. The configuration of the problem is presented in Figure 5, which depicts the reinforced A356 + 316L screen placed in a protective casing to prevent its movement. To calibrate the parameters of the computational model, we will utilize the work of [18], which provides experimental data on high-speed collisions of aluminum particles with five distinct screens. The numerical simulation of the collision processes permits to identification of the screens that exhibit adequate resilience against space debris particles. Additionally, we consider another three screens that can be produced using selective laser sintering of powders from the same materials as in [18]. The material properties for the aluminum alloys Al2017-T4 and A356 are taken from [44,45] and for steel 316L from [46]. Figure 4: Shock wave velocity vs. the mass velocity: 1—316L steel; 2—A356 aluminum alloy; 3—calculation according to the additive rule of mixtures; 4—direct numerical modeling in a metal matrix composite, 5—\(C_{\text{J}}\). Figure 3: A model of a volume-reinforced composite with an A356 matrix and 316L inclusions. For calculations, we will use the geometric dimensions of the impacting particle and screens from [18]. A spherical particle with a diameter of 1.9 mm made of the aluminum alloy Al2017-T4 with a mass of 10 mg moves at an initial speed of 6.0 km/s in all calculations. Every protective screen, with the exception of screen #2, has the same areal density. We evaluate the following protective screens:  
* Screen #1--a steel 316L plate, 4.5 mm thick;
* Screen #2--an A356 aluminum alloy plate, 12.0 mm thick;
* Screen #3--a two-layer plate made of 316L/A356, 7.5 mm thick (3.0/4.5);
* Screen #4--a two-layer plate made of A356/316L, 7.5 mm thick (4.5/3.0);
* Screen #5--a metal-matrix composite plate with the matrix composed of the A356 aluminum alloy and the volume reinforcement made of steel 316L, as is illustrated in Figure 3. The unit volume of the heterogeneous inclusion such a plate has a face-centered cubic (FCC) symmetry with a side length of 2.5 mm and a diameter of 0.8 mm. The screen thickness is 7.5 mm;
* Screens #6, #7, and #8 are considered later as alternatives;
* Screen #9--A356 aluminum alloy plate, 13.4 mm thick. The diameter of the protective screens in all calculations is 50.0 mm. Every protective screen, with the exception of screen #2, has the same areal density. All screens are placed in a protective casing to eliminate the influence of free lateral surfaces on the stress state of the screen materials. The effective volumetric concentration of steel in screens #3, #4, and #5 is 38%. The thicknesses and areal densities of the screens are listed in Table 1. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Screen** & **Material of the Screen** & **Density,** & **Areal Density,** & **Thickness,** \\  & **g/cm\({}^{3}\)** & **g/cm\({}^{2}\)** & **mm** \\ \hline \#1 [18] & Stainless steel 316L & 8.0 & 3.6 & 4.5 \\ \hline \#2 [18] & Aluminum alloy A356 & 2.7 & 3.24 & 12.0 \\ \hline \#3 [18] & Two-layer composite 316L/A356 & 4.8 & 3.6 & 7.5 \\ \hline \#4 [18] & Two-layer composite A356/316L & 4.8 & 3.6 & 7.5 \\ \hline \#5 [18] & Volume-reinforced composite & 4.8 & 3.6 & 7.5 \\ \hline \#6 & Uniform distribution of 316L steel grains in an A356 matrix & 4.8 & 3.6 & 7.5 \\ \hline \#7 & Direct gradient distribution of 316L steel grains in an A356 matrix & 4.8 & 3.6 & 7.5 \\ \hline \#8 & Inverse gradient distribution of 316L steel grains in an A356 matrix & 4.8 & 3.6 & 7.5 \\ \hline \#9 & Aluminum alloy A356 & 2.7 & 3.6 & 13.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the considered screens.