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.

The Bonded Discrete Element Method (BDEM) has raised interests in the graphics community in recent years because of its good performance in fracture simulations. However, current explicit BDEM usually needs to work under very small time steps to avoid numerical instability. We propose a new BDEM, namely Rod-BDEM (RBDEM), which uses Cosserat energy and yields integrable forces and torques. We further derive a novel Cosserat rod discretization method to effectively represent the three-dimensional topological connections between discrete elements. Then, a complete implicit BDEM system integrating the appropriate fracture model and contact model is constructed using the implicit Euler integration scheme. Our method allows high Young’s modulus and larger time steps in elastic deformation, breaking, cracking, and impacting, achieving up to 8 times speed up of the total simulation.