DIQ-MPM: Dual Interface Quadrature MPM for Simulating Large Deformation and Fluid-Solid Coupling

We present DIQ-MPM, a novel monolithic two-way coupling framework for simulating interactions between solids modeled with the total Lagrangian formulation and Eulerian incompressible fluids using the Material Point Method (MPM). Our approach combines an implicit TLMPM formulation with a mixed velocity-pressure scheme to robustly simulate compressible solids undergoing large deformations, while eliminating numerical fractures. To enable strong fluid-solid coupling without relying on overlapping grids, we introduce a Dual Interface Quadrature (DIQ) mechanism that maps fluid-solid interface information consistently between the current and reference configurations. This allows us to construct a unified sparse pressure-only system via Schur complement, leading to efficient and stable coupling. We also integrate a particle-based contact force model to resolve solid-solid and solid-boundary contacts within implicit TLMPM. Experimental results demonstrate that our method stably captures free-slip coupling, large deformation phenomena, and complex interactions between compressible solids and incompressible fluids.