A staggered grid multi–material arbitrary Lagrangian–Eulerian particle method for shock–structure interaction with dynamic fracture

Fluid-structure interaction modeling has garnered widespread attention in both academic research and engineering practice. Complex fluid-structure interaction problems involving shock waves, multi-material fluid flows, and structural dynamic fractures pose significant challenges to existing numerical methods. This paper presents a staggered grid multi-material arbitrary Lagrangian-Eulerian particle method, which strongly couples the staggered multi-material arbitrary Lagrangian-Eulerian method with the staggered grid material point method within a unified framework of staggered spatial discretization and cell-center quadrature. An auxiliary grid is constructed at the cell centers of the staggered multi-material arbitrary Lagrangian-Eulerian grid to accumulate immersed solid variables. Fluid and solid variables are assembled on the staggered multi-material arbitrary Lagrangian-Eulerian grid via cell-center quadrature, achieving implicit fluid-structure coupling and establishing a monolithic Lagrangian momentum equation. By combining the advantages of the staggered multi-material arbitrary Lagrangian-Eulerian method and the staggered grid material point method, the staggered grid multi-material arbitrary Lagrangian-Eulerian particle method is effective in solving complex fluid-structure interaction problems involving shock waves, multi-material fluid flows, and structural dynamic fractures. The accuracy and reliability of the staggered grid multi-material arbitrary Lagrangian-Eulerian particle method are verified through several numerical examples.