# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 4 Application in Explosion  
Explosions involve multi-material coupling at different stages, extreme deformation, damage, and fragmentation, and strong nonlinearity, posing significant difficulties and challenges for numerical simulation methods. It is challenging to simulate the process of gas product dispersion from explosive detonation using grid-based methods. In contrast, the MPM is adept at capturing the physical phenomena produced during the explosion impact process and is a very reliable numerical method for simulating explosions. [PERSON] et al. [45] were the first to demonstrate that the MPM can effectively simulate the physical processes of explosive detonation and successfully applied it to the impact of concrete-steel, Sedov-Taylor blast waves, and piston-container and piston-gas problems. To avoid numerical fragmentation and numerical noise in the standard MPM, [PERSON] et al. [46] proposed an adaptive MPM, where material points split into two when the cumulative strain in a certain direction exceeds a specified criterion (as shown in Figure 6). By simulating various explosive problems, such as explosively driven flyer plates and shaped charges, it was shown that MPM simulations can fit terminal velocities well and provide the entire deformation process under different conditions. To consider the lateral effects of planar sandwich structures, [PERSON] et al. [47] proposed a new modified Gurney solution that takes into account the lateral effects of planar sandwich structures, successfully simulating the explosion-driven metal problem. During explosions, interactions between fluids and solids are typically involved. To address this, [PERSON] et al. [48] developed an MPM for simulating the detonation of explosives involving fluid-structure interaction (FSI). [PERSON] et al. [49] applied the MPM to underwater explosion simulations, calculating the shock waves generated during the explosion and observing the diffusion process of the explosion. [PERSON] et al. [50] successfully modeled the fragmentation of plates and structural damage to ship hulls subjected to underwater contact explosions by implementing a staggered grid scheme to mitigate cell intersection noise and improve the precision of fluid simulations. The experimental findings were in concordance with the simulation results (see Figure 7). In explosion simulations, the boundary conditions at the interfaces between solid and fluid regions are often very complex. To effectively handle the issues at the multi-material interfaces, [PERSON] et al. [51] combined the advantages of the FDM and MPM to propose a coupled finite difference MPM (CFDMP). In the contact area, the MPM maps variables from the MPM background grid nodes to the FDM virtual points to provide boundary conditions for the FDM region; simultaneously, the FDM maps variables from the FDM cell center points to the MPM interface grid nodes to provide boundary conditions for the MPM region (see Figure 8). [PERSON] et al. [52] simulated the physical process of gas-solid flow in thermite explosions. To study the entire process, from continuous rock deformation to discontinuous fracturing and the evolution of explosions, [PERSON] et al. [53] proposed a coupling of the MPM and the continuum discontinuous element method (CDEM). The MPM was chosen to model the explosives, simulating the multi-physical phenomena involved in rock blasting, while the CDEM was used to model the rock material, simulating the dynamic fracturing  
Figure 6: Adaptive particle splitting scheme [46]. Figure 7: Final deformed configurations of the plate [50]. evolution of rocks. The contact model employs a particle-surface/edge contact approach (see Figure 9), and contact is established by meeting the following requirements:  
\[\left\{ \begin{aligned} d_{mn}&\leq R_{m}\\ d_{Bn}&\leq R_{BC}\\ d_{Cn}&\leq R_{BC}\end{aligned} \right.