# Research Advances in Large Deformation Analysis and Applications of the Material Point Method
## 7 Application in Fluid-Structure Interaction
In FSI problems, it is common for the solid region to undergo small deformations while the fluid region experiences large deformations. Therefore, some scholars have coupled the FEM and MPM to solve FSI problems. For example, [PERSON] et al. [104] proposed the coupled finite element MPM (CFEMP). When both MPM and FEM objects contribute to the same grid node, it indicates that the two objects are in contact at the grid node (see Figure 22). The feasibility of this method was verified by simulating the FSI model of a water column passing through an elastic barrier. The CFEMP contact algorithm requires consistent meshing between the FEM domain and the MPM domain, which can lead to excessive meshing in the FEM domain. To address this issue, [PERSON] et al. [105] employed  
Figure 20: Using a single set of material points to describe the two-phase response in the MPM [97]. a particle-to-surface contact algorithm and introduced a Coulomb friction model. [PERSON] and [PERSON] [106] used distributed interactive nodes on the finite element contact surface. [PERSON] et al. [107] introduced the v-p formulation into the CFEMP algorithm to solve numerical oscillation and volume locking issues in FSI problems. However, the CFEMP method still faces some challenges. For instance, when the contact surface is severely deformed, contact penetration is likely to occur. When contact forces act on each pair of contacting bodies, it is difficult to satisfy the contact conditions for all contact pairs simultaneously. To this end, [PERSON] et al. [108] proposed an improved local search method, a set of contact forces that satisfy the contact conditions for each contact pair, and successfully simulated the impact of a wedge entering water. To address the issues of a traditional MPM in solving FSI, such as the difficulty in imposing boundary conditions and low computational efficiency, [PERSON] et al. [109] proposed the immersed finite element MPM. In this method, the interaction between the MPM and FEM objects is handled using an immersed interface approach, with weighted tracking points set on the FEM object to efficiently track the FSI interface, as shown in Figure 23.  
Figure 21: Using two sets of material points to describe the two-phase response in the MPM [97]. Figure 22: Two-dimensional illustration of coupling the FEM with the MPM [104]. To avoid volumetric locking in the MPM, [PERSON] et al. [110] introduced the \(B\) method into the MPM-FEM model, discussing the impact of an inclined seabed on seepage resistance, soil flow patterns, lateral response, stress distribution, and failure mechanisms. Considering that fluid compressibility can cause the reflection of sound waves at boundaries, [PERSON] et al. [111] proposed an incompressible MPM and FEM coupling model to study the hydrodynamic characteristics of a triangular semi-submerged platform. This coupling scheme requires determining the specific locations of fluids and solids and classifying MPM background grid cells and solid finite elements, as shown in Figure 24. Evolving such complex FSI engineering typically requires significant computational costs, and there are no guarantees of accuracy. Non-slip boundary conditions can be conveniently implemented on the fluid-solid interface using the lattice Boltzmann method (LBM), which can simulate fluid flow problems simply and efficiently. Therefore, the LBM has been successfully applied to multiphase flows [112; 113], flow within porous media [114; 115], and turbulence [116; 117], among other issues. Based on this, [PERSON] et al. [118] proposed a coupled lattice Boltzmann-MPM (LBMPM) model, in which the LBM simulates fluid flow and the MPM simulates the dynamic large deformation of solids. [PERSON] et al. [119] expanded on this by using the LBM to handle binary fluid systems with large differences in density and viscosity, employing four sets of spatial  
Figure 23: Weighted tracing points (diamond shape dots) on the FEM element patches [109]. Figure 24: Schematic diagram of grid cell classification [111].