# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 3 Application in High-Speed Impact  
The structural damage process under high-speed collision often involves phenomena such as the generation and evolution of shock waves, the formation of debris clouds,  
Figure 4: Center velocity of the rolling cylinder over time [20]. and damage and destruction. The MPM has distinct advantages in handling fracture, fragmentation, and moving material interfaces, making it highly suitable for solving high-speed impact problems [26; 27]. [PERSON] et al. [28] were the first to validate the feasibility of the MPM in simulating hypervelocity impacts, proposing the explicit material point FEM. The material domain is discretized by finite element grids, with regular background grids defined in areas prone to large deformations. Once within the predefined background grids, nodes are converted into material points, which are then solved by the MPM. They successfully simulated the impact of an elastic rod on a rigid wall, cylinder impact tests, and the impact of spherical projectiles on thin and thick plates. To improve computational efficiency, [PERSON] et al. [29] made improvements by discretizing the material domain into blocks, simulating the dynamic response of a projectile impacting reinforced concrete, where the reinforcement bars were discretized into bar elements, and the concrete was discretized into material points (as shown in Figure 5). Furthermore, all steel reinforcement nodes and concrete particles move within the same single-valued velocity field. The particles at the nodes of the reinforcement elements carry only positional and velocity variables, while the reinforcement elements themselves bear the axial forces. By comparing with the literature, the combined advantages of the FEM and MPM were demonstrated. To prevent numerical oscillations caused by material points passing through grid boundaries, [PERSON] et al. [30] proposed the generalized interpolation MPM (GIMP) based on the Petrov-Galerkin method and successfully studied the dynamic response of a rod given an initial velocity impacting a rigid wall. Compared to the MPM simulation results, the solutions obtained by the GIMP are smoother and more continuous. [PERSON] et al. [31] introduced the convected particle domain interpolation technique into the MPM, employing a particle-particle contact algorithm to handle more complex high-speed impact and multi-body contact elastoplastic fracture problems. The SPH and the MPM are both meshless methods, with SPH already widely applied in the field of hypervelocity impacts [32; 33; 34]. To verify the MPM's capability in handling such problems, [PERSON] et al. [35] compared the accuracy and efficiency of the MPM and SPH through impact tube, Taylor rod, and debris cloud examples, indicating that SPH has difficulty in easily identifying debris boundaries, while the MPM scheme is more suitable for simulating the impact process at this stage. [PERSON] et al. [36] successfully simulated the fragmentation issues of cylinder explosions, the hypervelocity impacts of copper projectiles on copper targets, and collisions between two steel plates. [PERSON] et al. [37] simulated the large deformation of 7055 aluminum alloy plates under hypervelocity impacts from aluminum projectiles. [PERSON] et al. [38] investigated the morphology of the debris cloud,  
Figure 5: RC discretization in the FEMP method. Hollow dots denote concrete material points, while solid dots denote rebar nodes, and solid lines connecting solid dots denote rebar elements [29]. the size of perforations in a water-filled aluminum eggshell array structure, the residual velocity of the projectile, the impact energy, and the temperature field. Molecular dynamics (MD) simulations can track and simulate the dynamic evolution of a system by observing changes in atomic positions, velocities, forces, and other computable parameters [39]. In simulating high-speed impact problems, MD can simulate the mechanical behavior of materials at the atomic scale, but its capabilities are very limited. [PERSON] et al.