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

Fluid–structure interaction modelling 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 discretisation and cell-centre quadrature. An auxiliary grid is constructed at the cell centres 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-centre 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.