# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 7 Application in Fluid-Structure Interaction  
The FSI refers to the physical phenomena that occur when one or more solid structures interact with internal or surrounding fluid flow [85] (see Figure 19). Since the MPM algorithm can calculate fluids and solids within the same solution domain and has significant advantages in simulating large deformations and the fragmentation of fluids, many scholars have attempted to use it to address FSI problems. [PERSON] et al. [87] were the first to validate the feasibility of the MPM in FSI analysis. [PERSON] et al. [88] introduced the adaptive mesh refinement technique into the MPM and successfully simulated complex dynamic FSI problems in aerospace applications, further confirming the capability of the MPM in handling flows with complex geometries, large deformations, and FSI issues. However, the MPM solver has high requirements for computer performance. To efficiently and accurately simulate large-scale FSI problems, [PERSON] et al. [89] immersed MPM particles into the MMALE grid, achieving a strong coupling between the MMALE method and the MPM. They introduced a virtual velocity field near the FSI interface to update the stress of solid particles and proposed a local subdomain smoothing method to accelerate the remapping phase, which involves only the calculation of grid distortion regions. Finally, they validated the efficiency of this model in solving multiphase flow and FSI through examples. [PERSON] et al. [90] devised a hybrid data-driven framework supporting the popular and powerful MPM. They applied neural networks  
Figure 19: FSI categorized as a combination of fluid and solid domains [86]. Figure 18: Two-dimensional axisymmetric simulation model of steel ball penetration into gelatin [84]. to the MPM, achieving numerical acceleration while maintaining physical accuracy. This approach enables the efficient and accurate simulations of fluid-solid interactions in a data-driven manner. The multiphase MPM has been widely applied to simulate the interaction between porous soil and pore water, mainly based on two primary formulations. The first is the single-point formulation [91; 92], where material points carry all the information of both soil and pore water (see Figure 20), and the positions of material points are updated with the movement of the solid phase. [PERSON] et al. [93] proposed a three-phase single-point MPM, treating soil as a medium integrated with solid, liquid, and gas phases. [PERSON] et al. [94] enhanced the three-phase single-point MPM with a GPU acceleration framework and introduced cubic B-spline shape functions to improve numerical stability. To improve computational efficiency, [PERSON] et al. [95] neglected the gas phase, considering liquid acceleration and volume fraction gradients. [PERSON] et al. [96] developed a dynamic grid algorithm to optimize memory usage. The second is the two-point formulation [98; 99], which can use two sets of material points to represent the solid and liquid phases, respectively (see Figure 21), thus easily ensuring mass conservation for both phases and capturing their interactions. [PERSON] et al. [100] were the first to extend the two-phase two-point MPM to the dynamic analysis of porous media, using two sets of material points to represent the deformation of solids and pore fluids. [PERSON] and [PERSON] [101] developed a fully coupled MPM formulation that considers the relative acceleration between solids and fluids. To minimize numerical oscillations, [PERSON] et al. [102] employed the GIMP for spatial discretization and developed a three-dimensional two-phase two-point MPM code, successfully simulating fully saturated seepage failure. Building on [PERSON]'s work, [PERSON] et al. [103] developed a two-phase two-point MPM suitable for solving large deformations in both saturated and unsaturated soils. However, the presence of two sets of material points increases computational costs and requires the careful modeling of the interface, which limits the practical application of the MPM.